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Exam 13: Oscillations About Equilibrium

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Question 1

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A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27 cm and a frequency of 2.55 Hz. (a) What is the maximum speed of the needle? (b) What is the maximum acceleration of the needle?

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(A)20.3 CM...

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Question 2

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Both pendulum A and B are 3.0 m long. The period of A is T. Pendulum A is twice as heavy as pendulum B. What is the period of B?

A) 0.71T
B) T
C) 1.4T
D) 2T
E) 3T

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Question 3

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In simple harmonic motion, the speed is greatest at that point in the cycle when

The quartz crystal in a digital watch has a frequency of 32.8 kHz. What is its period of oscillation?

The position of a mass that is oscillating on a spring is given by x = (17.4 cm) cos[(5.46 s^-1)t]. Write an expression for the acceleration of the particle as a function of time.

A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves upward with constant acceleration?

A mass of 0.250 kg is attached to a spring and undergoes simple harmonic oscillations with a period of 0.640 s. What is the force constant of the spring?

A spar buoy is a cylindrical object that floats with its axis in the vertical direction. When it is disturbed a distance h from its equilibrium position, the magnitude of the restoring force is equal to ρghS, where ρ is the density of the water and S is the cross-sectional area of the cylinder. A certain spar buoy has a mass of 150 kg, a cross-sectional area of 2.50 m², and is floating in seawater, ρ = 1025 kg/m³. What is the frequency of ocean waves which will cause it to resonate?

FIGURE 13-1 -Curve A in Figure 13-1 represents

The position of a mass that is oscillating on a spring is given by x = (18.3 cm) cos[(2.35 s^-1) t]. What is the frequency of this motion?

For periodic motion, the maximum displacement from the equilibrium point is called the

Which of the following are characteristics of a mass in simple harmonic motion? I. The motion repeats at regular intervals. II. The motion is sinusoidal. III. The restoring force is proportional to the displacement from equilibrium.

A simple pendulum consists of a mass M attached to a weightless string of length L. For this system, when undergoing small oscillations

A child and an adult are walking. Their legs swing like physical pendulums and both swing through the same maximum angle. The adult is 1.5 times as tall as the child, and all their dimensions are scaled proportionately. They also have the same mass per unit volume. If the walking speed of the adult is 1.3 m/s, what is the walking speed of the child?

If you take a given pendulum to the Moon, where the acceleration of gravity is less than on Earth, the resonant frequency of the pendulum will

If the frequency of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum speed of the oscillator change?

A 16.2-g bullet with an initial speed of 870 m/s embeds itself in a 40.0-kg block, which is attached to a horizontal spring with a force constant of 1010 N/m. What is the maximum compression of the spring?

The time for one cycle of a periodic process is called the

A 1.5-kg mass attached to spring with a force constant of 20.0 N/m oscillates on a horizontal, frictionless track. At t= 0, the mass is released from rest at x= 10.0 cm. (That is, the spring is stretched by 10.00 cm.) (a) Determine the frequency of the oscillations. (b) Determine the maximum speed of the mass. Where does the maximum speed occur? (c) Determine the maximum acceleration of the mass. Where does the maximum acceleration occur? (d) Determine the total energy of the oscillating system. (e) Express the displacement as a function of time.

A mass on a spring undergoes SHM. When the mass passes through the equilibrium position, its instantaneous velocity