12. Suppose that an object is in simple harmonic motion given by13. Consider the following models of harmonic motion.(21 - ).yi = 5 sin(21 – 1)y = 5 sin 2Iy = 5 sin(21 – 3)Do both motions have the same frequency? What is the phasefor each equation? What is the phase difference? Are the(a) Find the amplitude, period, and frequency.(b) Find the phase and the horizontal shift.objects moving in phase or out of phase?

Given: An object is in simple harmonic motion given by the equation y=5Sin(2t-π/3) Introduction: The…

Answered: 12. Suppose that an object is in simple…

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter16: Oscillatory Motion And Waves

Section: Chapter Questions

Problem 19PE: Suppose a diving beard wi1h no one on it bounces up and down in a simple harmonic motion with a...

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Similar questions

Explain why you expect an object made of a stiff material to vibrate at a higher frequency than a similar object made of a spongy material.
Suppose a diving beard wi1h no one on it bounces up and down in a simple harmonic motion with a frequency of 4.00 Hz. The board has an effective mass of 10.0 kg. What is the frequency of the simple harmonic motion of a 75.0kg diver on the board?
At what positions is the speed of a simple harmonic oscillator halt its maximum? That is, what values of x/X give v=vmax/2, where X is the amplitude of the motion?
Consider the damped oscillator illustrated in Figure 15.19. The mass of the object is 375 g, the spring constant is 100 N/m, and b = 0.100 N s/m. (a) Over what time interval does the amplitude drop to half its initial value? (b) What If? Over what time interval does the mechanical energy drop to half its initial value? (c) Show that, in general, the fractional rate at which the amplitude decreases in a damped harmonic oscillator is one-half the fractional rate at which the mechanical energy decreases.
A small object is attached to the end of a string to form a simple pendulum. The period of its harmonic motion is measured for small angular displacements and three lengths. For lengths of 1.000 m, 0.750 m, and 0.500 m, total time intervals for 50 oscillations of 99.8 s, 86.6 s, and 71.1 s are measured with a stopwatch, (a) Determine the period of motion for each length, (b) Determine the mean value of g obtained from these three independent measurements and compare it with the accepted value, (c) Plot T2 versus L and obtain a value tor g from the slope of your best-fit straight-line graph. (d) Compare the value found in pan (c) with that obtained in pan (b).
Engineering Application: A suspension bridge oscillates with an effective force constant of 1.00108N/m. (a) How much energy is needed to make it oscillate with an amplitude of 0.100 m? (h) It soldiers march across the bridge with a cadence equal to the bridge’s natural frequency and impart 1.00104J of energy each second, how long does it take for the bridge's oscillations to go from 0.100 m to 0.500 m amplitude?
Some people think a pendulum with a period of 1.00 s can be driven with “mental energy“ or psycho kinetically, because its period is the same as an average heartbeat. True or not, what is the length of such a pendulum?
Show that the time rate of change of mechanical energy for a damped, undriven oscillator is given by dE/dt = bv2 and hence is always negative. To do so, differentiate the expression for the mechanical energy of an oscillator, E=12mv2+12kx2, and use Equation 15.51.
A 2.00-kg object is attached to a spring and placed on a frictionless, horizontal surface. A horizontal force of 20.0 N is required to hold the object at rest when it is pulled 0.200 m from its equilibrium position (the origin of the x axis). The object is now released from rest from this stretched position, and it subsequently undergoes simple harmonic oscillations. Find (a) the force constant of the spring, (b) the frequency of the oscillations, and (c) the maximum speed of the object, (d) Where does this maximum speed occur? (e) Find the maximum acceleration of the object. (f) Where does the maximum acceleration occur? (g) Find the total energy of the oscillating system. Find (h) the speed and (i) the acceleration of the object when its position is equal to one-third the maximum value.
The amplitude of a lightly damped oscillator decreases by 3.0% during each cycle. What percentage of the mechanical energy of the oscillator is lost in each cycle?

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