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# Draw the frequency-domain network and calculate o(t) in

ISBN: 9781118539293 159

## Solution for problem 8.25 Chapter 8

Basic Engineering Circuit Analysis | 11th Edition

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Basic Engineering Circuit Analysis | 11th Edition

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Problem 8.25

Draw the frequency-domain network and calculate o(t) in the circuit shown in Fig. P8.25 if i1(t) is 200 cos (105 t + 60) mA, i2(t) is 100 sin 105 (t + 90) mA, and S(t) = 10 sin (105 t) V. Also, use a phasor diagram to determine C(t). 30 250 nF i 1(t) i 2(t) + o(t) + + S(t) C(t) Figure P8.25

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Saturday, February 27, 2016 Week 7 Shared Syntactic Integration Resource Hypothesis • language processing in the brain • major structures • primary auditory cortex Broca’s area: speech production • • opercular and triangular parts of inferior frontal gyrus • Wernicke’s area: speech comprehension • posterior portion of superior temporal gyrus • arcuate fasciculus: ﬁbers connecting Broca’s and Wernicke’s area • music processing many areas • • pitch analysis in right temporal • primary and secondary auditory cortices in temporal relations • motor cortical areas involved in rhythm • connection between right temporal gyrus and frontal cortical areas important for working memory in music appreciation inferior frontal gyrus (Broca’s) involved in analysis of musical syntax • • syntactic vs. semantic processing in language • syntactic: how brain combines words into constituents and sentences • Broca’s area (regions in/around inferior frontal gyrus) • superior temporal gyrus/sulcus • left anterior temporal lobe semantic: how structural and semantic information is used in the understanding of • sentences • Wernicke’s area • inferior prefrontal cortex • syntax in music and language: • hierarchically organized sequences of basic elements language: phenomes, morphemes, words • • music: notes and chords • lower-level units arranged according to rules • language: complex words, phrases, sentences • music: motifs, phrases, movements • dependent on long-term memorized representations language: knowing lexical knowledge and the meaning of speciﬁc combinations of • words • music: memorizing familiar tunes as speciﬁc sequence • dissociation evidence: • aphasia: speech/language impaired in either auditory comprehension, verbal expression, reading/writing or functional communication patients that were aphasic after removal of left hemisphere or after stroke: • • restricted speech • able to recover word articulation with support of melody • due to the fact that language lateralized to left hemisphere BUT music in both (not necessarily true - new research) 1 Saturday, February 27, 2016 • overlap evidence: • BA 44 (part of Wernicke’s) activated in response to unexpected chords in music in music, activation is bilateral but only left in language • • posterior and anterior superior temporal cortex active in people who encounter unexpected chord/instrument • similar ERP patters to syntactic violations of language and harmonic deviations in music • theories of reconciliation: • how can neurological overlap exist alongside behavioral dissociation - relationship modular or shared • importance of comparative research • functional and neural architecture in both domains • role of different brain areas in hierarchical processing of complex sound sequences • broad principles of cognitive organization for complex info systems • shared syntactic resource integration hypothesis (SSIRH): language and music care a common set of processes that operate on different structural • representations • processing resources in frontal areas • representation regions in posterior brain areas • based on domain-speciﬁc cognitive theories of syntactic processing • comparative analysis best when driven by hypothesis, which requires consideration of empirically supported cognitive theory in both domains • dependency locality theory (DLT): • accounts for differences in complexity of grammatical sentences and for preferences in interpretation of syntactically ambiguous sentences • linguistic syntax requires: • structural storage: keeping track of predicted syntactic categories (expect verb after noun) • structural integration: connecting words to prior words • predicts that processing cost increases with distance between incoming elements and site of integration • processing cost = integration cost + storage cost • generates numerical predictions of syntactic processing • correspond to empirical data from reading time experiments • sentences presented and time taken to read each word • time taken to read each words corresponds with processing cost predicted by DLT • tonal pitch space theory (TPS): • both musicians and non musical have highly structured mental representation of musical pitch • quantiﬁes tonal distance between 2 chords in musical sequence based on distance in structured cognitive space • “stable” pitches and chords perceived as closer to each other • separate keys perceived in orderly sets of distances from each other • numerical predictions of perceived tension • perceperception of tonal distance inﬂuences predicitions of the perceived ebb and ﬂow of tension in musical sequences • tonal distance increases with tonal distance between chords • numerical predictions of TPS correspond to “tension proﬁling” scores produced by subjects who rate tension over time in a musical passage (listerners perceive musical elements in hierarchical relations) 2 Saturday, February 27, 2016 • convergence of domain-speciﬁc cognitive theories • structural integration (connecting x to y) is a key part os syntactic processing integration depends on distance between x and y in abstract cognitive space • • activatoin based framework • x —> y activates representation of x (incoming input) and reactivates T (prior input) • shared integration resource • processing resources serve to rapidly and selectively bring low-activation representations up to activation threshold for integration to occur neural areas and operations shared • • integration takes place in distinct regions • corrresponding neural overlap • not yet known • required within subjects comparative studies of language and music using localization techniques design domain-independent tasks with two distinct levels of syntactic integration • demands (quantiﬁed with DLT and TPS operations) • use fMRI to search for brain regions which show increased activation as a function of integration cost in both domains • existing evidence for shared integration resource • language processing research (Kaan & Swab, 2002; Haarmann & Kolk, 1991) processing regions in frontal areas provide resources for computations in posterior • areas where syntactic representations reside • MEG data (Koelsch, et al., 2000 & 2001) • activation of Broca’s area in harmonic processing • ERP component analysis (Patel, et al., 2007) • domain-independent tasks elicited statistically indistinguishable P600s • evidence for sidtinct representation regions • cases of music-speciﬁc syntactic deﬁcits (Grifﬁths, et al., 1997; Peretz, 1993 & 1994) • associated with damage to superior temporal gyri • thought to be important in long-term representation of harmonic relations • congenital amusia (Ayotte, et al., 2002) • due to a problem with ﬁne-grained pitch discrimination • suggests developmental failure to form cognitive representations of pitch • linguistic priming: how processing is inﬂuenced by a word’s syntactic or semantic relation to a passage • harmonic priming: inﬂuence of harmonic context on the processing of a target chord due to the acoustic similarity and the its distance in the cognitive construct • regions of activation • shared resources • anterior cingulate and medial frontal cortex • Domain general attention mechanisms (Slevc and Okada, 2014) • speech speciﬁc activation • bilateral anterior temporal gyrus • supports implication in combinatorial semantic processing, NOT hierarchical structures (Wong and Gallate, 2012) • conﬂicting activation in broca’s area • differences in activation based on tasks • passive listening • discrimination task 3 Saturday, February 27, 2016 • memory task • Music Task vs Passive Speech Listening Music discrimination – Passive speech listening • • No difference in activation of pars triangularis • Music memory – Passive speech listening • Greater activation of pars triangularis with music memory • reasoning for differences in activation • supporting Shared Synaptic Integration Resource Hypothesis overlapping activation seen when increased resources are need to complete the • speech or music task • Additional Support- cognitive control • Shared resources for linguistic and music processing in re-analyzing information and in conﬂict resolution (Slevc and Okada, 2014) • applications of SSIRH: improves treatments of speech disorders • Somatosensory Systems review ﬁgure 67c in Hendelman atlas • • modalities: • touch: discriminative, ﬂutter vibration, crude touch • proprioception: where we are in space, muscle length and tension • temperature • nociception sensations of touch begin at the skin • • epidermis (outer layer) • dermis (inner layer) • mechanoreceptors • sense touch - mechxnosensitive ion channels • in organs - artery distension, stretch in digestive organs and bladder rapidly adapting: for discriminative touch • • ﬁre at onset and offset of stimulus, not during • slowly adapting: for sensing steady pressure • ﬁre the entire duration • types: • Pacinian corpuscles: in superﬁcial subcutaneous layers, muscles, joints, internal organs • • end in nerve endings inside connective tissue • vibrations go through concentric layers to nerve endings to open mechanically gated ion channels • large receptive ﬁelds • rapidly adapting signal changes in pressure or sudden movement • • Meissner’s corpuscles: • superﬁcial • inside connective tissue • 2 point discrimination • rapidly adapting 4 Saturday, February 27, 2016 • small receptive ﬁelds • Rufﬁni endings: • deep skin layers • enlarged nerve endings • sense steady skin pressure (stretch, tension) • slowly adapting • large receptive ﬁelds Merkel’s disks: • • superﬁcial • enlarged nerve endings • sense steady pressure • slowly adapting • free nerve endings • respond to mechanical, thermal or noxious stimulation • generally for nociception • two point discrimination • higher density of mechanoreceptors (in hands and face, especially ﬁngertips) • small receptive ﬁelds more cortical tissue devoted to these areas • • may be special mechanisms • lateral somatosensory tissue: info from hands and face small receptive ﬁeld large receptive ﬁeld fast adaptation Meissner’s corpuscle Pacinian corpuscle slow adaptation Merkel’s disk Rufﬁni’s ending • muscle spindle: stretch receptor • senses muscle length - proprioceptors are the LARGEST and FASTEST conducting axons • proprioceptor mechanoreceptors are in joints AND information from the muscle • Golgi tendon organs send info about tension on a muscle • sensory info comes from muscles, which then feeds info back into the motor system • primary afferent axons Aa (group I): • • highly myelinated • largest (13-20 um) and fastest (80-120 m/s) • proprioception in skeltl muscles (because you need to be able to react quickly to where your body is in space • transmit to spinal cord from proprioceptive system • NOT present in skin • AB (group II): • large and myelinated (not as big as Aa) • 30-70 m/s • mechanical stimulus Pacinian corpuscles • • touch info from SKIN (mechanoreceptors) • Ad (group III) • small, myelinated 5 Saturday, February 27, 2016 • 5-30 m/s • cold temperature fast pain information - sharp and localized • • C ﬁbers (group IV) • small, unmyelinated • .5-2 m/s • mechanical stimulus - slow pain (dull aches) • temperature, itch dermatome: receptive ﬁelds - areas of the skin innervated by the left and right dorsal roots • • adjacent dorsal roots can innervate overlapping areas • demonstration: shingles • lesions or sores on skin activated on a speciﬁc nerve, so delineated within this area • pathways: • information sensed on skin, sent to spinal cord via ﬁbers somatosensory info: • • from Pacinian corpuscles • less myelinated • cell bodies in dorsal root ganglion • information goes up spinal cord in dorsal columns to medulla and brainstem • collaterals also sent off for reﬂexive stimulation (in spinal cord) proprioceptive info • • highly myelinated • from muscle spindles • cell bodies in dorsal root ganglion • info goes up spinal cord in dorsal columns to medulla and brainstem • crosses in medulla • collaterals sent off for reﬂexive information • pain and temperature (via Ad and c ﬁbers) • cell bodies in dorsal root ganglion • synapses in lamina of dorsal root • crosses immediately in dorsal horn and travels in contralateral side of spinal cord • spinothalamic pathway (aka anterolateral system) • somatotopic arrangement for information • lower extremities MEDIAL (Gracile fascicle) • sacral and lumbar • upper extremities lateral (cuneate fasciculus) • thoracic and cervical • in medulla, information synapses in gracile (lower) and cuneate nuclei (upper) • don’t have cuneate fascicles until thoracic level of spinal cord • cervical information enteres last • crosses midline in medulla, travels to thalamus • tactile pathway: • primary neurons from periphery (receptors) synapse in gracile or cuneate nucleus of medulla • dorsal columns in lower spinal cord are small, get bigger as you travel up the spinal cord • below medulla: dorsal columns - once above medulla pathway is called the medial lemniscus • secondary neuron: travels through pons and midbrain (brainstem) from medulla 6 Saturday, February 27, 2016 • synapses in ventroposterior lateral nucleus of thalamus • once at level of medial lemniscus, ventral in medulla at pons, lemniscus moves more dorsally again • • at level of midbrain, lemniscus is not more lateral • now medial lemniscus and anterolateral systems travel together • tertiary neuron: from thalamus to primary somatosensory cortex • anterolateral system (ALS): spinothalamic tract • travels to ventral posterolateral nucleus of thalamus (VPL) crossed immediately in spinal cord • • pain information DIRECTLY to VPL • reticulothalamic: information from neurons that project to reticular nuclei (medullary or pons reticular system) • synapse in intralaminar nuclei of thalamus (centromedian and parafascicular) • underlie alterting mechanism to painful stimuli involved in arousal and sleep/wake cycles • • different modalities processed on different parts of the gyrus: • area 3B: • primary somatic sensory • dense inputs from VP • very responsive to somatic input electrical stimulation evokes sensory experiences • • lesions impair somatic sensation • area 3A: sense of body position • area 1: input from 3B (texture) • area 2: size and shape • posterior parietal: polymodal information • most inputs terminate in layer IV - projections to other layers (stacked in columns) • homunculus: mapping of receptive ﬁelds of SI neurons produces orderly organization of information • info from speciﬁc body area terminates in speciﬁc brain region • columns of neurons devoted to one particular receptor type • cortical map plasticity: • surrounding areas invade cortical areas that lose innervation • ex: remove a ﬁnger and the cortical areas for the ﬁngers around it expand to ﬁll the area • larger cortical areas for greater stimulation in periphery • spinocerebellar tract: on both sides • proprioceptive information from periphery to cerebellum • posterior: lower limb and trunk • cuneocerebellar: upper limbs • synapse in lateral cuneate nucleus • anterior: touch info to cerebellum • crosses twice • rostral: upper limb 7 Saturday, February 27, 2016 Pain Systems Pain: an unpleasant sensory and emotional experience associated with actual or potential • tissue damage or described in terms of tissue damage, or both • types of nociceptors: • free nerve endings of unmyelinated c ﬁbers and lightly myelinated Ad ﬁbers • mechanical: strong pressure (crude touch) • thermal: extreme temperature chemical: histamines (itch) and others • • polymodal • hyperalgesia: increased sensitivity after injury • pain receptors: sensitize after injury • lower threshold and more responsive (more AP) • allodynia: perceiving innocuous stimuli as painful after tissue damage • involves vasodilation due to release of substance p • comparison of Ad and c ﬁbers • ﬁrst pain sensation registered by Ad axons (FAST) • pin prick • longer-lasting pain sensation mediated by c ﬁbers (SLOW) • slow, dull, muscle pain • somatotopic organization: • lower extremities - lateral • upper extremities - medial • laminae in the dorsal horn • Ad into lamina I (posteromarginal nucleus) and V • c ﬁbers into II (substantia gelatinosa) • III and IV - non noxious (nucleus proprius) • gate theory: • laminae that receive inputs from Ad and C ﬁbers also get input from AB ﬁbers • non-nociceptive ﬁbers indirectly inhibit the effects of the pain ﬁbers • this closes gate to transmission of stimuli (weakens signal sent to the thalamus) • anterolateral system (ALS): spinothalamic tract • travels to ventral posterolateral nucleus of thalamus (VPL) • crossed immediately in spinal cord • pain information DIRECTLY to VPL • reticulothalamic: information from neurons that project to reticular nuclei (medullary or pons reticular system) • synapse in intralaminar nuclei of thalamus (centromedian and parafascicular) • underlie alterting mechanism to painful stimuli • involved in arousal and sleep/wake cycles • therapies for intractable pain • thalamic lesioning (CM-PF) • deep brain stimulation • descending pain control: can selectively modulate pain in different areas • regulated by emotion and behavioral state • somatosensory cortex • insula and anterior cingulate • periventricular nucleus • periaqueductal gray (stimulation causes analgesia) 8 Saturday, February 27, 2016 • raphe nuclei • pain perception involves cognitive processes cortico-limbic striatal circuits: leads to autonomic reactivity • • cognitive appraisal • emotional reaction • behavioral response attention • pain neuromatrix: leads to thalamocortical relays • ACC, insula, PFC. amygdala, hypothalamus, sensory cortex leads to inﬂammatory and bimolecular mediators • • also leads to autonomic reactivity • can also control descending pain modulation • noxious stimulus leads to stimulation of nociceptor —> dorsal horn of the spine • leads to thalamocortical relays • activation of medial prefrontal cortex (mPFC) and posterior cingulate cortex (PCC) in pain rumination 9

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Draw the frequency-domain network and calculate o(t) in