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Find an equation that relates 2% settling time to the

Control Systems Engineering | 7th Edition | ISBN: 9781118170519 | Authors: Norman J. Nise ISBN: 9781118170519 162

Solution for problem 72 Chapter 4

Control Systems Engineering | 7th Edition

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Control Systems Engineering | 7th Edition | ISBN: 9781118170519 | Authors: Norman J. Nise

Control Systems Engineering | 7th Edition

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Problem 72

Find an equation that relates 2% settling time to the value of f v for the translational mechanical system shown in Figure P4.19. Neglect the mass of all components. [Section: 4.6]

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1. Community All the interacting animal and plant species in a habitat. Includes feeding relations 2. Spatial heterogeneity hypoth More species BC tropical comms are in areas that are more physically complex More niches 3. Guild Subset of community Species distinguished by location or method of obtaining food 4. Tropic structure Largest emergent prop Allows questions on how efficient energy flow is between levels 5. Food chains Links of pop relationships Btwn 3­9 links Can determine max number of trio box levels by determining the longest food chain 6. Food web Many interacting and interconnected food chains 7. Macrophytes Aquatic vascular plants w roots 8. POM Particulate organic matter Dead leaves stems and dead animal bodies Fungi and bacteria 9. DOM Dissolved organic matter Dissolves organic mols from living and dead legs (Lipids sugars AAs) Serves as energy source for detrivores 10. Alpha diversity ...species diversity Depends on species richness(S) and species evenness 11. Species evenness Percentage of indivs in community of each species 12. Diversity Number species in community and relative freqs of each species 13. Disturbance succession predation comp mutualism time scales spacing scales number of microhabs special heterogeneity climate conds and habitat stability Factors affecting diversity 14. Alpha diversity Species diversity within one site or location 15. Shannon weaver index (H) H=(sum of) Piln(pi) P=importance value(proportion of individuals in species) I­total sample of indivs from quad from: pi=ni/N Gives more weight to rare species 16. Importance value of Shannon weaver eq I­total sample of indivs from quad from: pi=ni/N Ni=number indivs in ith species N=total number of indivs from all species .... Neg sum of first eq 17. Evenness value for Shan­weaver Eh=H/Hmax H=Shan­weaver diversity index Proportional to ln(species number) So... N1=e^H Hmax=ln(S) S=number of species ... Varies from 0 to 1 18. Number of species eq from Shan­weaver N1=e^H 19. Simpsons index (N2) prob of randomly selected indiva being diff ... N2=number of equally common species needed to produce same diversity value as observed in the common N2=1/(sum of all pi^2) .. Ranges from 1 to S Gives less weight to rare species and more weight to common ones 20. Total size of comm resource axis inc...so additional species can be added into come In resource overlap of each species w out changing niche breadth of species ... Inc comp so productivity of each species dec but can pack more in species Inc specialization.. Make niche breadth narrow Avg prod of species Dec so more niches available Ways to add new species to a community 21. Evenness index for Simpson index Ed=N2/S Ranges from 0 to 1 Each species repd by same number of indivs 22. Gamma diversity Total number of species counted in broad geographical area 23. Beta diversity Change in community composition as you move from one place or another Measure of rate of species change between 2 or more communities Or measure of similarity of two communities 24. Soreson similarity index Beta diversity eq CC=2c/(a+b) A : number of species recorded in one community B: .... In second comm C: number of species in common to both comms 25. Greater species richness in tropically for all phylogenic lineages 26. George Simpson Notes 5 diff factors that affected dive rusty gradients of North American mammals N/s gradient not smooth.. Some mammalian groups more diverse in temperate Zone Topographical relies affected by diversity Rocky Mts and Appalachians support more species that would be at that given latitude E/w trends existed in diversity... More species in w part of continent than e There were areas of abrupt changes associated w mt ranges Peninsular lows exist... Fewer species present on them that's on adj continentals 27. Time hypoth Tropical areas ancient roots of diversity Longer geological history.. More speciation Speciation occurred during ice age .... Wallace thought so too 28. Competition hypoth Greater comp in tropics so niche partitioning and character displacement/release Niche overlap larger 29. David lack Saw example of character displacement .. Bird beak w diff size seeds Character release when each species along on island 30. Predation hypoth Predation severe in tropics so predators keep comp exclusion from occurring .. Weak competitors go extinct 31. Dan jazen... Pear pressure hypoth Hypoth by ___ that says specialized pests concentrate on parent tree Seeds only survive far from parent tree Seed comp very high by parent tree 32. Disturbance hypoth Suggest moderate disturbance impedes xome exclusion so greater diversity Intermediate disturbance amt best 33. Geographic area hypoth Greater species richness of tropics due to significantly larger land areas 34. John terborgh Saw annual air temp more uniform high and constant over broad range of latitudes ... 25n to 25s lat 35. Michael rosenzweig Withinf tropic area much larger area pops could be larger Allopatric speciation more likely 36. Stephen Forbes Published lake as A microcosm Recognized for topic of biological comm Lake is complex machine.. Org... Bat selection worked out species diff by bat selection so looks in equilibrium 37. Henry cowles Examined long term change in plant community Succession works in predictable manner Dunes rarely covered by lake Two most imp factors physiograohy and control exerted by plants 38. Shelford and Clements Argues organismal or holistic view of communities Species are parts and develop Immunities sharply defined units where species always occurred together Argues communities are closed... Ecological limit similar for all species in comm, always o cud together 39. Seral stage Two patches of Same assoc similar in species comp at one point in time 40. Orgs and comms interacting parts ... Continue thru time and develop predictable and orderly pattern... Like life and death ... Have physiology and can reproduce... Adapt to change so in dynamic eq Developed forest classification ... Can ID org as member of given assoc Clements ideas concerning similarity between org and organismal comm 41. Gleason Opp of Clements idea.. Individualistic comm view Similarities btwn comm and legs superficial Not orderly Species distributed Indiv Open comm­ More of artifact from overlapping species distrib 42. Ecotones Region of rapid replacement of species along environmental gradient ... Transition zone between two diff habitat types Sharp in closed comms 43. Species continuum concept Within broad geographical areas species replace each other gradually along gradients of phys conds 44. Curtis and Whittaker Each species has distinct and unique locations ___ saw gradients and a continuum on analysis of forest vegetation ___ saw little evidence of closed comm when studying changes in species comp .. Species have their own tolerance range 45. Old field succession Type of secondary succession where disturbance has reset comm and succession resets comm and starts over 46. Pioneer community and climax comm 2 endpoint sod communities observed at beginning and end of succession respectively 47. Autogenic succession Succession from biotic intxs among living orgs of community caused by plants and animals themselves 48. Allogenic succession Caused by changes in physical or abiotic components of ecosystem 49. primary succession begins from rock.substrate.. no soil/plants 50. secondary succession when disturbance event has partially cleared/opened an envir plants/animals/soil present 51. colonizers/pioneers r selected species well adapted for good dispersal and short life and high reproductive rates "weeds" 52. shade intolerant early colonizer species are usually ___ ___ 53. 10­50 50­100 100 some larger trees become dominate veg after ___­__ years woody trees after __­___ mature forest after ___` 54. k selected adapted for conds where comp is high.. larger w few seeds and repeated reprod seasons 55. climaz comm final seral stage 56. allelopathy chems that inhibit growth of other plants, even own seedlings. can build up in soil c 57. clements develeoped monoclimax theory ­said climate alone det'd climax comm ­14 diff zones in NA 58. monoclimax theory mature comm that continually replaces itself indef was natural and viewd as closed comm 59. polyclimax theory tansley theory that says local climax may be goverened by variety of factors... particulary soil conds, but also climate, fire, and topography ....comms could be similar by __ 60. whittaker climax pattern theory theory that open climax comms common, composition depends on envir conds vary gradually along gradient by ___ 61. connel and slatyer proposed 3 contrating models as mechs that cause autogenic succession facilitation, inhibition & tolerance 62. clements facilitation model by ___ 63. facilitation theory succession is developmental seq ...first species makes envir less suitable for themselves succession mediated by early species 64. egler inhibition model by ___ 65. inhibition model estbl'd species tend to suppress new colonists pioneer species make envir less susceptible for invasion by other species succession not totally predictable and no distinct climax comm speces i replacement inhibited by previous colonists until latter are killed/weakened 66. tolerance model model by ___ and ___ says succession leads to species most eff at using resources each species can invade new habitat equally more eff slower growing comp species wait out short lived 67. intermed distrubance hypoth patches of undistrubed areas in climac stage allow few indivs of pioneer specccies to live at climax stage div may dec 68. plants __ determine base for food web, so affects animal types(animals passive followers) 69. riverine zonationin interplay of succession and distrubance in allogenic succession 70. riverine succession rivers and lakes/sandbar sides­>scoured site(herbs)­>short lived grasses and trees)­> at height river doesnt cross veg changes to trees ect­> climax xomm(oak hickory maple) 71. marine envir succession small algae­>seaweed­>barnacles & mussels ­> dom species(crabs seastars) allelopathic chems disturbances 72. hariston, smith & slobodkin HSS hypth also called "world is green" hypoth that says herbivores not considered food limited so compete for resources preds keep them in check plants limited by comp "top down" control by ___ ___ and ___ 73. top down control/trophic cascade effect indirect effects 74. oksanen ecosystem exploitation hypoth hypoth by __ also called "world is white/yellow/green hypoth" that says low prod areas scarce. Herbs have little effect on plants, so comp high w/ them inc prod causes herb comp and top down impact on plants carniv inc to control herbs so plants inc 75. bottom up controls changes in lower level trophic orgs alter abundance of species comp of higher levels occurs from changes in nutrient availability/limitations and autotrophic prod of plants animals trophic cascade has no effect 76. world is prickly and tastes bad murdoch " _____ " by ___ world is green but ... plants have chem/morph traits to make them uneatable herbs food limited, so fierce comp strong bottom up control 77. envir stress hypoth menge & sutherland hypoth that says physdisturbance, predation, and comp governed by envir stress low complexity in food web as envir becomes benign, top down strength inc 78. keystone preds top carnivore that selectively feeds on lower levels, loweing their pop size... reduces comp exclusion/extinction 79. elim of kestones comp can cause trophic cascade and dec habitat complexity/diversity ... if this happens when species is removed then it is keystone pred 80. ecosystem engineer org that sig created, modifies, or maintains/destroys phys habitat so affects species fversityhabitati/ heterogeneity 81. allogenic ecosystem engineer.. beavers & elephants engineer type that change phys envir by transforming.. create habitat or maintain land habitats over time ex) ___ & ____ 82. autogenic ecosystem engineers corals kelps/large trees engineers that change envir using parts of their phy bodies(dead and alive) create habitat for other species as they grow ex) 83. yellowstone park area became open from elk overgrazing when wolves removed...when put back elk pop dropped & moved back to higher elevation, veg recovered berry plants inc, inverts inc, bears inc diet of berries some species recovered coyoyte pop dec, antelope inc, more beavers returned and built dams (stabilize water flow, red erosion, ret water, created riparian habitat) 84. mustelids badgers and wolverines 85. elton said comm stability greater in more diverse comms ­pest outbreaks more common in simples ­species go extinct ­ " invasions occur more ­ species rich trop forests less insect outbreak ­ numerical stabilitynu 86. numerical stability diff to maintain constant numbs of indiv in simple comms 87. macarthur more trophic links present in comm show more stability... inc resistance to change ­extinction doesnt effect as much if pred can change prey bc variety of choices to eat numerically stable max trophic level at connectance 88. connectance C=L[{(S)(S­1)}/2] l= # feeding links S=species richness max possible amt of links from 0 to 1 high C= more stable 89. may said math model shows inc complexity reduces stability disturbance of one species may effect others inc in diveristy may make indiv species more vulnerable but total biomass of ecosystem stabilized in more complex ecosystem bc other species can compensate more constant=more stable 90. equilibrium when pop size and comm S stay constant over time ­comp and pred in density dep fashion to reg pop size ­high resilience, species deletion stability, and persistance stability ­saturated w species so species invasion rare 91. noneq pop size vary drastically, to extinction ­density depd biotic processes...regulation rare ­ low score on all stability tyoes ­lots of invasion ... composition changes ­disturbances dom factors limiting/affecting comm 92. local stability tendancy of comm to return to original state after small disturbance 93. global stability ecosystem returns to orginal state after large disturbance 94. ability of comm to withstand variation little change when altered measures prod/biomass 95. forest resistance trees can withstand change in climate and sharp envir disturbances 96. factors causing resistance food storage scale of disturbance 97. resilience speed that a disturbed system returns to original eq rapid return=high resilience slow=low 98. resilient system may not be resistant, & vice versa 99. island geography looked at the connection btwn island size and species # that could be supported 100. circular __ shaped islands are better for diversity 101. down up immigration lines curve __ on graph and extinction lines curve __ 102. S balanced when E=I species # reaches some eq & stays constant w time large islands have more niches and less extinctions closer islands have higher immg rates MW theory assumptions 103. simberloff & wilson fumigated islands to see how they were recolonized 104. tansley ___ coined "___" as the sum total of all intxs of a comm including among themselves and with th eenvir 105. lindeman __ said ecosystems were energy transforming system to ecology ­trophic layers ­law of thermodynamics hold true for orgs in trophic levels 106. lindeman efficiency amt of energy taken in at N levle, relative to the amt of energy taken in by the trophic lvl below (N­1) 107. pyramid of numbers created by counting all the indivs of one trophic level... can be inverted 108. pyramid of Energy cant be inverted(would violate law of thermodyns) amt of E produced at one lvl is greater than the lvl above less E reaches higher trophic lvls bc it is used up for work at lower lvls 109. biomass pyramid rep's mass at each trophic lvl cna be inverted more biomass can be produced at producer lvl over time 110. Odums described comm as E transforming machines Championed use of E as common currency for describing commas & ecosystems 111. Total E budget eq for an indiv C=F+U+R+Pg+Pr C=consumed E F=egested material not used (feces) U=energy lost in E content of urine R=respiration, basal met And work Pg=growth of new tissues Per=reproduction 112. Odum Wrote Fundamentals of Ecology 113. Energy budget for animal: T=NC+C T=total amt of E at one tropic lvl of food web that is available to the next NM­ unused energy not harvested at next level C= gross energy inttake(amt consumed by animal) 114. Assimilated E Found by subtracting energy that remains in feces(ingested food) ­total amt ingested food 115. Metabolize lie E E used for resp, growth, and reprod M=R+P 116. Energy budget eq Thermodynamic eq that described E flow thru indiv , pop, or community 117. Lineman efficiency The product of exploitation efficiency, assimilation efficiency, and net production efficiency 118. Exploitation efficiency Food energy ingested/energy in prey population =(C/T)x100 119. Assimilation efficiency Food E assimilated/food energy ingested =(A/C)x100 120. Net production efficiency E used in growth & reprod/food energy assimilated =(P/A)x100 121. Ecological efficiency(lindeman efficiency) E in growth and reprod/e in lower tropic lvl =(P/T)x100 122. Exploitation efficiency Inc w higher tropic lvls =(C/T)x100 123. 20% of sunlight hitting earth is absorbed by atmosphere aand 30% radiates back to space Only 1% strikes plants Other 99% drives earth processes ...but not captured and converted into ATP energy 124. Gross primary prod (GPP) Amt of e fixed by photosynth in as community 125. Net primary prod (NPP) GPP­e lost through plant respiration ... Only 1­5%s of e that strikes plants is converted into biomass by photosynth 126. Light does not limit rate of prod in terrestrial systems...exceeds saturation pts 127. Terrestrial plant prod inc w amt of evapotranspiration (measure of water in ecosystem) Length of Growing season also correlates w prod 128. N & P N before p P __ & ___ levels limit prod in many terrestrial ecosystems __ occurs before __ But in tropical systems _ limits 1st 129. Light can be limiting in aquatic envirs, as well as nutrients 130. Herbivore Carnivores __ EE ranges from 1­10%(greater than plants 1­5%) ___ EE's ranges from 10­90% 131. Physiological ecologists ___ ecologists are particularly interested in the assimilation efficiencies and production efficiencies 132. Inc Carnivores Detrivores Assimilation efficiencies tend to ___ w higher tropic lvls AE=(A/C)x100=(R+P+U)/Cx100 Tells how well an animal is assimilating materials and quality of food the animal is eating __ _have highest AE at 60­90% __ below 15%(& wood eating animals) Herbivore AE depends on part of plant eaten seeds­80% Browsers 30­60% 133. Prod efficiencies ___ dec w higher tropic lvls 134. coprophagy chew cud or produce special feces they redigest 135. endotherms orgs at higher trophic lvls w lower prod efficiency but higher assimilation efficiency 136. ectotherms orgs at lower trophic lvls w higher prod efficiency but lower respiration costs 137. 90 travel long distances endothermic carnivores use up to _% or more of their assimlated E in resp bc (2 reasons) so have low NPE 138. 1­5 5­30 ecological efficiencies for endotherms __% and %_ for ectotherms (Pprey/Ppre)d x 100 139. 10% efficiency of E transfer __% of E passed to next org in food chain ...also called the 140. vitousek estiamted humans use ~20% world's terrestrial NPP 141. C:N if detrius has a high _:_ ratio, decomposition is slow ex) in peat bogs 142. herbivores microbivores/bacteriovores microbivores in almost all comms, the production of detrivores is higher than __ many detrivores are ____/___ many herbivores are actually ___ 143. resource anything we get from the phys envir to meet needs/wants 144. 80% a nonrenewable resource usually considered economically depleted when about __ of its estimated supply is extracted and used or if it is too expensive to extract the last of it from Earth 145. pollution changes in resources due to usually small amts of naturally produced pollution and additional changes from human activity 146. human produced pollutants: concentrated in certain area artificially produced produced in great quantities direct/indirect harmful effects less easily decomposed by nat processes so persist in envir 147. compartments components of the nutrient cycle, including resource pools/sinks/orgs 148. flux movement of nutrients btwn compartments and their magnitudes 149. system part of universe that can be isolated and studied 150. open system exchanges factors or materials w other systems 151. closed sysemwt here one factor does not exchange w others 152. positive feedback loop where an inc in the output of a system leads to further inc in output....destabilizes system 153. negative feedback when output of a system shuts off its response... stabilizing 154. hutton theory of uniformitization...said we can predict future envir changes based on the past 155. avg residence time measure of time it takes for any/all of resources in a reservior to be moved thru the system 156. slower large systems w long residence times are __­ to chance than smaller ones 157. hubbard brook experimental forest gene likens amt of nutrients in flux is small in comparison to size of resource pools in ecosystems turnover rates small in undisturbed sites and nutrients are retained experiment bu __ 158. oxygen cycle largest compartment: earth crust 2nd largest: atmosphere 2 main routes of cycling: thru rock weathering & burial of organic mats 159. photosynth and breakdown of water 2 main producers of oxygen 160. ozone depletion ozone shield major component of oxygen cycle produced from photochem rxs 90% found in stratosphere( also called ___) 161. molina and roland hypoth that CFCs are depleting ozone in stratosphereby ___ 162. fts of CFC theory: CFCs emitted in lower stratosphere very stable(100 yr residulal time) CFCs destroyed in statosphere by UV so form Cl ions that rxs w ozone ozone blocks UVB ozone formed by UVC inc in UV reaching earht is adverse affect(cancer/dec prod) 163. major emissions of chems that deplete ozone: halocarbons(CFCs)­ 83% C tetrachloride 8% methyl chloroform 5% ...methylbromide 164. each cl atom destroys ~100k mols of ozone in 1­2 yrs cl cant be removed from atmosphere easily 165. potential envir factors related to ozone depletion damage to food chains human health effects more UV 166. 1/5 ___ of sunlight striking earth is used to change water to liquid form 167. evap less than rain over land, but opp over ocean 168. 26 in avg of __ inches of rainfall per m ^2 per yr tunover time for water in atmopsphere is 2 weeks 169. erlich 26 __ calculated that __% of freshwater on earth is used by humans 170. 1­5billion ___ tons of CO2 added per yr 171. winter(high photosynth) summer high points of co2 cycle in __ and low in ___ ...connected to E flwo 172. global warming various mols in atmosphere act as heat blanket and retard heat flux into space 173. CO2, methane. nitrous oxides, CFCs, ozone imp greenhouse gases 174. 450ppm 2­5 global warming effects: by 2050 CO2 lvls will be ___, it will be warmer by __C, wetter/drier, water warm/dry up, floods/droughts in same areas higher sea lvl inc in storms ice sheets melting ecological comm changes disease heat death exotic species spread diff T inc global warming 175. plant prod would inc w higher [CO2] 176. loss changes in rainfall from global warming will cause net __ of cropland and declines in crops 177. reasons for sea level rising from global warming: thermal expansion of warming ocean waters ice 178. 100 for very 1C inc in T, climate belts will shift __miles N in N hemisphere 179. nitrogen cycle cycle w many redox rxs 180. nitrification NH3­­>NO2­ ­­> NO3­ by nitrifying bac.. use ammonia 181. denitrification NO3­­> N2 use nitrates fungi 182. ammonification organic N(proteins)­­>NH3 breaks down proteins and AAs bac/fungi 183. N fixation N2­­>NH3 bluegreen bac do 90% N fixation 184. assimilation NH3/NO3­ to N(proteins) incorporate N into plants­­>animal proteins 185. dead zones from fertilizer runoff.. in ocean 186. P cycle phosphate major limiting factor bc no atomospheric component needed for: met, reprod, & growth primarly found as __(in bird duano/bat guano) 187. sulfur cycle has redox rxs can cause acid rain(sulfur dioxide & hydrogen sulfur) 188. acid rain rain w ph under 5.6 ...could cause lakes to drop to ph 2 189. causes of acid rain: N oxides and Sdioxides formed from rx w atmospheric water vapor and oxygen pollutants in atmosphere sulfides(coal/fossil fuels) 190. buffer acid rain effects more pronounced in areas where soil/bedrock cant ___ acid input 191. acid rain in lake dissolves chems needed for life & leave lake w water outflow ..intereferes w reprod, algae, and fish food 192. pimm __ came up w ideas of species deletion stability and persistence stability 193. species deletion stability if one species removed in complex comm, removal of top pred bad,but removal of basal plant inc stability higher C=shorter return time more complex=more stable 194. persistence stability how long system lasts before changed to new state/eq habitat loss could cause extinction invading species cant get in(more complex=harder invasion) complex C=higher stability 195. biological comm S(species diversity) # and type of guilds & relative abundance/dominance of orgs 196. physical comm plant type dictactes __ ___ ­components of ___: plant type, orgs, leaf types, seasonality of plants 197. tilman said inc in diversity benefits ecosysttems as whole bc stabilizes system and inc prod pops in more diverse fluctuate more than in simple more diverse=more resistance 198. species diversity affected by: disturbance, envir heterogeneity, recruitment 199. andrewartha & birch animal comms det'd by harsh abiotic facs of phys envir(weather) 200. random process of colonization/disturbance dets presence/absence of animal species 201. disturbance any event that disrupts something changes resources, substratum availability, phys envir 202. intermediate disturbance hypoth connell hypoth by __­ that explained tropic diversity infreq/small events­ eliminates inferior competitors(dec diversity) strong/freq­ dominant competitors elim, colonizing species w high dispersal are there(dec diversity) intermediate­ dom and colonizing there so highest div 203. huston used computer sims to show diversity is highest w moderate disturbance too few­ competitive exclusion too freq­only seral stage weedy plants 204. sousa said disturbance forms gaps so comm div high at mid successional seq ex) overturned boulders green algae­­> one overrides others eventually 205. hutchinson "paradox of plankton" asked why so many plankton in water column constant envir change so no comp exclusion so can coexist 206. macarthur & wilson developed eq theory of island biogeography

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Chapter 4, Problem 72 is Solved
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Textbook: Control Systems Engineering
Edition: 7
Author: Norman J. Nise
ISBN: 9781118170519

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