"At t = 0, a 785-g mass at rest on the end of a

If a particle undergoes SHM with amplitude 0.18 m, what is the total distance it travels in one period?

An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the spring constant k of this elastic cord?

The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets into the drivers seat. If the car goes over a humn. what will be the frecmencv o f oscillations? Tpnore

What is the equation describing the motion of a mass on the end of a spring which is stretched 8.8 cm from equilibrium and then released from rest, and whose period is 0.66 s? (b) What will be its displacement after 1.8 s?

Estimate the stiffness of the spring in a childs pogo stick if the child has a mass of 35 kg and bounces once every 2.0 seconds.

A fishermans scale stretches 3.6 cm when a 2.4-kg fish hangs from it. (a) What is the spring stiffness constant and (b) what will be the amplitude and frequency of oscillation if the fish is nulled down 5 cm more and released so that it

Tall buildings are designed to sway in the wind. In a 100-km/h wind, for example, the top of the 110-story Sears Tower oscillates horizontally with an amplitude of 15 cm. The building oscillates at its natural frequency, which has a period of 7.0 s. Assuming SHM, find the maximum horizontal velocity and acceleration experienced by a Sears employee as she sits working at her desk located on the top floor. Compare the maximum acceleration (as a percentage) with the acceleration due to gravity.

Construct a Table indicating the position x of the mass in Fig. 14-2 at times t = Q ,\T ,\T ,\T ,T , and T, where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave?

A small fly of mass 0.25 g is caught in a spiders web. The web oscillates predominately with a frequency of 4.0 Hz. (a) What is the value of the effective spring stiffness constant k for the web? (b) At what frequency would you expect the web to oscillate if an insect of mass 0.50 g were trapped?

A mass m at the end of a spring oscillates with a frequency of 0.83 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of ml

A uniform meter stick of mass M is pivoted on a hinge at one end and held horizontal by a spring with spring constant k attached at the other end (Fig. 14-28). If the stick oscillates up and down slightly, what is its frequency? [Hint. Write a torque equation about the hinge.] FIGURE 14-28 Problem 11.

A balsa wood block of mass 55 g floats on a lake, bobbing up and down at a frequency of 3.0 Hz. (a) What is the value of the effective spring constant of the water? (b) A partially filled water bottle of mass 0.25 kg and almost the same size and shape of the balsa block is tossed into the water. At what frequency would you expect the bottle to bob up and down? Assume SHM.

Figure 14-29 shows two examples of SHM, labeled A and B. For each, what is (a) the amplitude, (b) the frequency, and (c) the period? (d) Write the equations for both A and B in the form of a sine or cosine.

Determine the phase constant 0 in Eq. 14-4 if, at t = 0, the oscillating mass is at (a) x = A, (b) x = 0, (c) x = A, (d) x = \A , (e) x = - \A , ( f )x = A /V l .

A vertical spring with spring stiffness constant 305 N/m oscillates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (y = 0) with positive velocity at t = 0. (a) What equation describes this motion as a function of time? (b) At what times will the spring be longest and shortest?

The graph of displacement vs. time for a small mass m at the end of a spring is shown in Fig. 14-30. At t = 0, x = 0.43 cm. (a) If m = 9.5 g, find the spring constant, k. (b) Write the equation for displacement x as a function of time.FIGURE 14-30 Problem 16.

The position of a SHO as a function of time is given by x = 3.8 cos(5-7r/4 + tt/6) where t is in seconds and x in meters. Find (a) the period and frequency, (b) the position and velocity at t = 0, and (c) the velocity and acceleration at t = 2.0 s.

A tuning fork oscillates at a frequency of 441 Hz and the tip of each prong moves 1.5 mm to either side of center. Calculate (a) the maximum speed and (b) the maximum acceleration of the tip of a prong.

An object of unknown mass m is hung from a vertical spring of unknown spring constant k, and the object is observed to be at rest when the spring has extended by 14 cm. The object is then given a slight push and executes SHM. Determine the period T of this oscillation

A 1.25-kg mass stretches a vertical spring 0.215 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?

Consider two objects, A and B, both undergoing SHM, but with different frequencies, as described by the equations xA= (2.0m)sin(2.01) and xB = (5.0m) sin(3.01), where t is in seconds. After t = 0, find the next three times t at which both objects simultaneously pass through the origin.

A 1.60-kg object oscillates from a vertically hanging light spring once every 0.55 s. (a) Write down the equation giving its position y (+ upward) as a function of time t, assuming it started by being compressed 16 cm from the equilibrium position (where y = 0), and released, (b) How long will it take to get to the equilibrium position for the first time? (c) What will be its maximum speed? (d) What will he its maximum arrp.lp.ratinn and where will it first he

A bungee jumper with mass 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 43.0 s. He finally comes to rest 25.0 m below the level of the bridge. Estimate the spring stiffness constant and

A block of mass ra is supported by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 14-31). What will be the frequency of vertical oscillation? FIGURE 14-31 Problem 24.

A mass m is connected to two springs, with spring constants /q and k2, in two different ways as shown in Fig. 14-32a and b. Show that the period for the configuration shown in part (a) is given by r = + h) and for that in part (b) is given by T = 277 J m V k\ + k2 Ignore friction.FIGURE 14-32 Problem 25.

A mass ra is at rest on the end of a spring of spring constant k .A t t = 0 it is given an impulse / by a hammer. Write the formula for the subsequent motion in terms of ra, k, J, and t.

A 1.15-kg mass oscillates according to the equation x = 0.650 cos 7.40* where x is in meters and t in seconds. Determine (a) the amplitude, (b) the frequency, (c) the total energy, and (d) the kinetic energy and potential energy when x = 0.260 m.

(a) At what displacement of a SHO is the energy half kinetic and half potential? (b) What fraction of the total energy of a SHO is kinetic and what fraction potential when the displacement is one third the amplitude?

Draw a graph like Fig. 14-11 for a horizontal spring whose spring constant is 95 N/m and which has a mass of 55 g on the end of it. Assume the spring was started with an initial amplitude of 2.0 cm. Neglect the mass of the spring and any friction with the horizontal surface. Use your graph to estimate (a\ the notential enerov. (h\ the kinetic enerov.

A 0.35-kg mass at the end of a spring oscillates 2.5 times per second with an amplitude of 0.15 m. Determine (a) the velocity when it passes the equilibrium point, (b) the velocity when it is 0.10 m from equilibrium, (c) the total energy of the system, and (d) the equation describing the motion of the mass, assuming that at * = 0, x was a maximum.

It takes a force of 95.0 N to compress the spring of a toy popgun 0.175 m to load a 0.160-kg ball. With what speed will the ball leave the gun if fired horizontally?

A 0.0125-kg bullet strikes a 0.240-kg block attached to a fixed horizontal spring whose spring constant is 2.25 X 103N/m and sets it into oscillation with an amplitude of 12.4 cm. What was the initial speed of the bullet if the two objects move together after impact?

If one oscillation has 5.0 times the energy of a second one of equal frequency and mass, what is the ratio of their amplitudes?

A mass of 240 g oscillates on a horizontal frictionless surface at a frequency of 3.0 Hz and with amplitude of 4.5 cm. (a) What is the effective spring constant for this motion? (b) How much energy is involved in this motion?

A mass resting on a horizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. It takes 3.6 J of work to compress the spring by 0.13 m. If the spring is compressed, and the mass is released from rest, it experiences a maximum acceleration of 15 m/s2. Find the value of (a) the spring constant and (b) the mass.

An object with mass 2.7 kg is executing simple harmonic motion, attached to a spring with spring constant k = 280 N/m. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s. (a) Calculate the amplitude of the motion, (b) Calculate the maximum speed attained by the object.

Agent Arlene devised the following method of measuring the muzzle velocity of a rifle (Fig. 14-33). She fires a bullet into a 4.648-kg wooden block resting on a smooth surface, and attached to a spring of spring constant k = 142.7 N/m. The bullet, whose mass is 7.870 g, remains embedded in the wooden block. She measures the maximum distance that the block compresses the spring to be 9.460 cm. What is the speed v of the bullet?FIGURE 14-33 Problem 37.

Obtain the displacement x as a function of time for the simple harmonic oscillator using the conservation o f enerav F ns 1410. \Hi nt Tntearate F.n. 1411a with

"At t = 0, a 785-g mass at rest on the end of a horizontal spring (k = 184 N/m) is struck by a hammer which gives it an initial speed of 2.26 m/s. Determine (a) the period and frequency of the motion, (b) the amplitude, (c) the maximum acceleration, (d) the position as a function of time, (e) the total energy, and ( /) the kinetic energy when x = 0.40A where A is the amplitude."

A pinball machine uses a spring launcher that is compressed 6.0 cm to launch a ball up a 15 ramp. Assume that the pinball is a solid uniform sphere of radius r = 1.0 cm and mass m = 25 g. If it is rolling without slipping at a speed of 3.0 m/s when it leaves the launcher, what is the spring constant of the spring launcher?

A pendulum has a period of 1.35 s on Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that on Earth?

A pendulum makes 32 oscillations in exactly 50 s. What is its (a) period and (b) frequency?

A simple pendulum is 0.30 m long. At t = 0 it is released from rest starting at an angle of 13. Ignoring friction, what will be the angular position of the pendulum at (a) t = 0.35 s, (b) t = 3.45 s, and (c) t = 6.00 s?

What is the period of a simple pendulum 53 cm long (a) on the Earth, and (b) when it is in a freely falling elevator?

A simple pendulum oscillates with an amplitude of 10.0. What fraction of the time does it spend between +5.0 and -5.0? Assume SHM.

Your grandfather clocks pendulum has a length of 0.9930 m. If the clock loses 26 s per day, how should you adjust the length of the pendulum

Derive a formula for the maximum speed vmax of a simple pendulum bob in terms of g, the length , and the maximum angle of swing 0max.

A pendulum consists of a tiny bob of mass M and a uniform cord of mass m and length L (a) Determine a formula for the period using the small angle approximation. (b) What would be the fractional error if you use the formula for a simple pendulum, Eq. 14-12c?

The balance wheel of a watch is a thin ring of radius 0.95 cm and oscillates with a frequency of 3.10 Hz. If a torque of 1.1 X 10_5m-N causes the wheel to rotate 45, calculate the mass of the balance wheel.

The human leg can be compared to a physical pendulum, with a natural swinging period at which walking is easiest. Consider the leg as two rods joined rigidly together at the knee; the axis for the leg is the hip joint. The length of each rod is about the same, 55 cm. The upper rod has a mass of 7.0 kg and the lower rod has a mass of 4.0 kg. (a) Calculate the natural swinging period of the system, (b) Check your answer by standing on a chair and measuring the time for one or more complete back-andforth swings. The effect of a shorter leg is a shorter swinging period, enabling a faster natural stride.

(a) Determine the equation of motion (for 0 as a function of time) for a torsion pendulum, Fig. 14-18, and show that the motion is simple harmonic. (b) Show that the period T is T = 2 irV l/K . [The balance wheel of a mp.nhaninal watr.h is an p.Yamnlfi of a torsion nenrhihim

"A student wants to use a meter stick as a pendulum. She plans to drill a small hole through the meter stick and suspend it from a smooth pin attached to the wall (Fig. 14-34). Where in the meter stick should she drill the hole to obtain the shortest possible period? How short an oscillation period can she obtain with a meter stick in this way? FIGURE 14-3"

A meter stick is hung at its center from a thin wire (Fig. 14-35a). It is twisted and oscillates with a period of 5.0 s. The meter stick is sawed off to a length of 70.0 cm. This piece is again balanced at its center and set in oscillation (Fig. 14-35b). With what period does it oscillate?FIGURE 14-35 Problem 53.

An aluminum disk, 12.5 cm in diameter and 375 g in mass, is mounted on a vertical shaft with very low friction (Fig. 14-36). One end of a flat coil spring is attached to the disk, the other end to the base of the apparatus. The disk is set into rotational oscillation and the frequency is 0.331 Hz. What is the torsional spring constant K ( t = K 6 ) lFIGURE 14-36 Problem 54.

A plywood disk of radius 20.0 cm and mass 2.20 kg has a small hole drilled through it, 2.00 cm from its edge (Fig. 14-37). The disk is hung from the wall by means of a metal pin through the hole, and is used as a pendulum. What is the period of this pendulum for small oscillations?FIGURE 14-37

A 0.835-kg block oscillates on the end of a spring whose spring constant is k = 41.0 N/m. The mass moves in a fluid which offers a resistive force F = bv, where b = 0.662 N* s/m. (a) What is the period of the motion? (b) What is the fractional decrease in amplitude per cycle? (c) Write the displacement as a function of time if at t = 0, x = 0, and at t = 1.00 s, x = 0.120 m.

Estimate how the damping constant changes when a cars shock absorbers get old and the car bounces three times after going over a speed bump.

A physical pendulum consists of an 85-cm-long, 240-g-mass, uniform wooden rod hung from a nail near one end (Fig. 14-38). The motion is damped because of friction in the pivot; the damping force is approximately t proportional to d6/dt. The rod is set in oscillation by displacing it 15 from its equilibrium position and releasing it. After 8.0 s, the amplitude of the oscillation has been reduced to 5.5. If the angular displacement can be written as 6 = Ae~yt costo't, find (a) 7, (b) the approximate period of the motion, and (c) how long it takes for the amplitude to be reduced to \ of its original value. FIGURE 14-38 Problem 58.

A damped harmonic oscillator loses 6.0% of its mechanical energy per cycle, (a) By what percentage does its frequency differ from the natural frequency f 0 = (l/27r) Vfc/m? (b) After how many periods will the amplitude have decreased to 1/e of its original value?

A vertical spring of spring constant 115 N/m supports a mass of 75 g. The mass oscillates in a tube of liquid. If the mass is initially given an amplitude of 5.0 cm, the mass is observed to have an amplitude of 2.0 cm after 3.5 s. Estimate the damping constant b. Neglect buoyant forces.

(a) Show that the total mechanical energy, E = \mv2 + \k x 2, as a function of time for a lightly damped harmonic oscillator is E = IkJpe-W^ = E0<T(6/m)*, where Eq is the total mechanical energy at t = 0. (Assume c1)' b/2m.) (b) Show that the fractional energy lost per period is A E _ 2irb _ 2tt E mo)Q Q where <w0 = V/c/m and Q = mwo/6 is called the quality factor or Q value of the system. A larger Q value means the system can undergo oscillations for a longer time.

A glider on an air track is connected by springs to either end of the track (Fig. 14-39). Both springs have the same spring constant, k, and the glider has mass M. {a) Determine the frequency of the oscillation, assuming no damping, if k = 125 N/m and M = 215 g. (b) It is observed that after 55 oscillations, the amplitude of the oscillation has dropped to one-half of its initial value. Estimate the value of y, using Eq. 14-16. (c) How long does it take the amplitude to decrease to one-quarter of its initial value?FIGURE 14-39 Problem 62.

(a) For a forced oscillation at resonance (&> = &>0), what is the value of the phase angle <j>0 in Eq. 14-22? (b) What, then, is the displacement at a time when the driving force Fext is a maximum, and at a time when Fext = 0? (c) What is the phase difference (in degrees) between the driving force and the displacement in this case?

Differentiate Eq. 14-23 to show that the resonant amplitude peaks at b2 2m2

An 1150 kg automobile has springs with k = 16,000 N/m. One of the tires is not properly balanced; it has a little extra mass on one side compared to the other, causing the car to shake at certain speeds. If the tire radius is 42 cm, at what speed will the wheel shake most?

Construct an accurate resonance curve, from to = 0 to w = 2o)0, for Q = 6.0.

The amplitude of a driven harmonic oscillator reaches a value of 23.7F0/k at a resonant frequency of 382 Hz. What is the Q value of this system?

By direct substitution, show that Eq. 14-22, with Eqs. 14-23 and 14-24, is a solution of the equation of motion (Eq. 14-21) for the forced oscillator. [Hint. To find sin <f)0 and cos </>0 from tan <f>0 , draw a right triangle.]

Consider a simple pendulum (point mass bob) 0.50 m long with a Q of 350. (a) How long does it take for the amplitude (assumed small) to decrease by two-thirds? (b) If the amplitude is 2.0 cm and the bob has mass 0.27 kg, what is the initial energy loss rate of the pendulum in watts? (c) If we are to stimulate resonance with a sinusoidal driving force, how close must the driving frequency be to the natural frequency of the pendulum (give A/ = / - / 0)?

A 62-kg person jumps from a window to a fire net 20.0 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple spring, (a) Calculate how much it would stretch if the same person were lying in it. (b) How much would it stretch if the person jumped from 38 m?

An energy-absorbing car bumper has a spring constant of 430 kN/m. Find the maximum compression of the bumper if the car with mass 1300ko collides with a wall at a sneed of

The length of a simple pendulum is 0.63 m, the pendulum bob has a mass of 295 g, and it is released at an angle of 15 to the vertical, (a) With what frequency does it oscillate? (b) What is the pendulum bobs speed when it passes through the lowest point of the swing? Assume SHM. (c) What is the total energy stored in this oscillation assuming no losses?

A simple pendulum oscillates with frequency / . What is its frennencv if the entire nendnhim accelerates at 0.50 p

A 0.650-kg mass oscillates according to the equation x = 0.25 sin(5.50?) where x is in meters and t is in seconds. Determine (a) the amplitude, (b) the frequency, (c) the period, (d) the total energy, and (e) the kinetic energy and potential energy when x is 15 cm.

A crane has hoisted a 1350-kg car at the junkyard. The cranes steel cable is 20.0 m long and has a diameter of 6.4 mm. If the car starts bouncing at the end of the cable, what is the period of the bouncing? [Hint: Refer to Table 12-1]. (b) What amplitude of bouncing will likely cause the cable to snap? (See Table 12-2, and assume Hookes law holds all the way up to the breaking point.)

An oxygen atom at a particular site within a DNA molecule can be made to execute simple harmonic motion when illuminated by infrared light. The oxygen atom is bound with a spring-like chemical bond to a phosphorus atom, which is rigidly attached to the DNA backbone. The oscillation of the oxygen atom occurs with frequency / = 3.7 X 1013 Hz. If the oxygen atom at this site is chemically replaced with a sulfur atom, the spring constant of the bond is unchanged (sulfur is just below oxygen in the Periodic Table). Predict the frequency for a DNA molecule after the sulfur substitution.

A seconds pendulum has a period of exactly 2.000 s. That is, each one-way swing takes 1.000 s. What is the length of a seconds pendulum in Austin, Texas, where g = 9.793 m /s2? If the pendulum is moved to Paris, where g = 9.809 m/s2, by how many millimeters must we lengthen the pendulum? What is the length of a seconds pendulum on the Moon, where g = 1.62m/s2?

A 320-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, it sinks 3.5 cm deeper into the water. When he steps off, the raft oscillates for a while, (a) What is the frequency of oscillation? (b) What is the total energy of oscillation (ignoring damping)?

At what displacement from equilibrium is the speed of a SHO half the maximum value?

A diving board oscillates with simple harmonic motion of frequency 2.5 cycles per second. What is the maximum amplitude with which the end of the board can oscillate in order that a pebble placed there (Fig. 14-40) does not lose contact with the board during the oscillation?FIGURE 14-40 Problem 80.

A rectangular block of wood floats in a calm lake. Show that, if friction is ignored, when the block is pushed gently down into the water and then released, it will then oscillate with SHM. Also, determine an equation for the force constant.

A 950-kg car strikes a huge spring at a speed of 25 m/s (Fig. 14-41), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the spring? (b) How long is the car in contact with the spring before it bounces off in the opposite direction?

A 1.60-kg table is supported on four springs. A 0.80-kg chunk of modeling clay is held above the table and dropped so that it hits the table with a speed of 1.65 m/s (Fig. 14-42). The clay makes an inelastic collision with the table, and the table and clay oscillate up and down. After a long time the table comes to rest 6.0 (a) What is the effective spring constant of all four springs taken together? (b) With what maximum amplitude does the platform oscillate? FIGURE 14-42 Problem 83.

In some diatomic molecules, the force each atom exerts on the other can be approximated by F = C/r2 + D/r3, where r is the atomic separation and C and D are positive constants, (a) Graph F vs. r from r = 0.8D/C to r = 4D/C. (b) Show that equilibrium occurs at r r0 D/C. (c) Let Ar = r r0 be a small displacement from equilibrium, where A r r0. Show that for such small displacements, the motion is approximately simple harmonic, and (d) determine the force constant. (e) What is the period of such motion? [Hint: Assume one atom is kept at rest.]

A mass attached to the end of a spring is stretched a distance x0 from equilibrium and released. At what distance from equilibrium will it have (a) velocity equal to half its maximum velocity, and (b) acceleration equal to half its maximum acceleration?

Carbon dioxide is a linear molecule. The carbon-oxygen bonds in this molecule act very much like springs. Figure 14-43 shows one possible way the oxygen atoms in this molecule can oscillate: the oxygen atoms oscillate symmetrically in and out, while the central carbon atom remains at rest. Hence each oxygen atom acts like a simple harmonic oscillator with a mass equal to the mass of an oxygen atom. It is observed that this oscillation occurs with a frequency of / = 2.83 X 1013 Hz. What is the spring constant of the C O bond?FIGURE 14-43 Problem 86, the C 0 2 molecule.

Imagine that a 10-cm-diameter circular hole was drilled all the way through the center of the Earth (Fig. 14-44). At one end of the hole, you drop an apple into the hole. Show that, if you assume that the Earth has a constant density, the subsequent motion of the apple is simple harmonic. How long will the apple take to return? Assume that we can ignore all frictional effects. [Hint: See Appendix D.] FIGURE 14-44

A thin, straight, uniform rod of length = 1.00 m and mass m = 215 g hangs from a pivot at one end. (a) What is its period for small-amplitude oscillations? (b) What is the length of a simple pendulum that will have the same period?

A mass m is gently placed on the end of a freely hanging spring. The mass then falls 32.0 cm before it stops and begins to rise. What is the frequency of the oscillation?

A child of mass m sits on top of a rectangular slab of mass M = 35 kg, which in turn rests on the frictionless horizontal floor at a pizza shop. The slab is attached to a horizontal spring with spring constant k = 430 N/m (the other end is attached to an immovable wall, Fig. 14-45). The coefficient of static friction between the child and the top of the slab is fx = 0.40. The shop owners intention is that, when displaced from the equilibrium position and released, the slab and child (with no slippage between the two) execute SHM with amplitude A = 0.50 m. Should there be a weight restriction for this ride? If so, what is it?FIGURE 14-45 Problem 90.

Estimate the effective spring constant of a trampoline.

In Section 14-5, the oscillation of a simple pendulum (Fig. 14-46) is viewed as linear motion along the arc length x and analyzed via F = ma. Alternatively, the pendulums movement can be regarded as rotational motion about its point of support and analyzed using r = la. Carry out this alternative analysis and show that 0(0 0r where 6(t) is the angular displacement of the pendulum from the vertical at time t, as long as its maximum value is less than about 15.FIGURE 14-46 Problem 92.

A mass m on a frictionless surface is attached to a spring with spring constant k as shown in Fig. 14-47. This mass-spring system is then observed to execute simple harmonic motion with a period T. The mass m is changed several times and the associated period T is measured in each case, generating the following data Table:Mass m (kg) Period T (s) 0.5 0.445 1.0 0.520 2.0 0.630 3.0 0.723 4.5 0.844 (a) Starting with Eq. 14-7b, show why a graph of T2 vs. m is expected to yield a straight line. How can k be determined from the straight lines slope? What is the lines ^-intercept expected to be? (b) Using the data in the Table, plot T2 vs. m and show that this graph yields a straight line. Determine the slope and (nonzero) ^-intercept, (c) Show that a nonzero ^-intercept can be expected in our plot theoretically if, rather than simply using m for the mass in Eq. 14-7b, we use m + m0, where m0 is a constant. That is, repeat part (a) using m + ra0 for the mass in Eq. 14-7b. Then use the result of this analysis to determine k and m0 from your graphs slope and ^-intercept. (d) Offer a physical interpretation for m0, a mass that appears to be oscillating in addition to the attached mass m.FIGURE 14-47 Problem 93.

Damping proportional to v2. Suppose the oscillator of Example 14-5 is damped by a force proportional to the square of the velocity, damping = ~cv2, where c = 0.275 kg/m is a constant. Numerically integrate* the differential equation from t = 0 to t = 2.00 s to an accuracy of 2%, and plot your results.