054 O In Fig. 15-49a, a metal plate is mounted on an axle through its center of mass. A spring with k = 2000 N/m connects a wall with a point on the rim a distance r= 2.5 cm from the center of mass Initially the spring is at its rest length. If the plate is rotated by 7° and released, it rotates about the axle in SHM, with its angular position given by Fig. 15-49b.The horizontal axis scale is set by t, = 20 ms. What is the rotational inertia of the plate about its center of mass? e (deg) t (ms) 10 (a) (6)

054 O In Fig. 15-49a, a metal plate is mounted on an axle through its center of mass. A spring with k = 2000 N/m connects a wall with a point on the rim a distance r= 2.5 cm from the center of mass Initially the spring is at its rest length. If the plate is rotated by 7° and released, it rotates about the axle in SHM, with its angular position given by Fig. 15-49b.The horizontal axis scale is set by t, = 20 ms. What is the rotational inertia of the plate about its center of mass? e (deg) t (ms) 10 (a) (6)

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter16: Oscillations

Section: Chapter Questions

Problem 68PQ: Consider the system shown in Figure P16.68 as viewed from above. A block of mass m rests on a...

See similar textbooks

Similar questions

A diver on a diving board is undergoing SHM. Her mass is 55.0 kg and the period of her motion is 0.800 s. The next diver is a male whose period of simple harmonic oscillation is 1.05 s. What is his mass if the mass of the board is negligible?
Check Your Understanding Identify an object that undergoes uniform circular motion. Describe how you could trace the SHM of this object.
Suppose a diving board with no one on it bounces up and down in a SHM with a frequency of 4.00 Hz. The board has an effective mass of 10.0 kg. What is the frequency of the SHM of a 75.0-kg diver on the board?
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 12.28.
If a car has a suspension system with a force constant of 5.00104 N/m , how much energy must the car’s shocks remove to dampen an oscillation starting with a maximum displacement of 0.0750 m?
Refer to the problem of the two coupled oscillators discussed in Section 12.2. Show that the total energy of the system is constant. (Calculate the kinetic energy of each of the particles and the potential energy stored in each of the three springs, and sum the results.) Notice that the kinetic and potential energy terms that have 12 as a coefficient depend on C1 and 2 but not on C2 or 2. Why is such a result to be expected?
Check Your Understanding Identify one way you could decrease the maximum velocity of a simple harmonic oscillator.
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?
Give an example of a simple harmonic oscillator, specifically noting how its frequency is independent of amplitude.
An automobile with a mass of 1000 kg, including passengers, settles 1.0 cm closer to the road for every additional 100 kg of passengers. It is driven with a constant horizontal component of speed 20 km/h over a washboard road with sinusoidal bumps. The amplitude and wavelength of the sine curve are 5.0 cm and 20 cm, respectively. The distance between the front and back wheels is 2.4 m. Find the amplitude of oscillation of the automobile, assuming it moves vertically as an undamped driven harmonic oscillator. Neglect the mass of the wheels and springs and assume that the wheels are always in contact with the road.
The temperature of the atmosphere oscillates from a maximum near noontime and a minimum near sunrise. Would you consider the atmosphere to be in stable or unstable equilibrium?
Can this analogy of SHM to circular motion be carried out with an object oscillating on a spring vertically hung from the ceiling? Why or why not? If given the choice, would you prefer to use a sine function or a cosine function to model the motion?