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Exam 14: Oscillations

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Question 31

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A ball is oscillating on an ideal spring with an amplitude of 8.3 cm and a period of 4.6 s. Write an expression for its position, x, as a function of time t, if x is equal to 8.3 cm at t = 0.0 s. Use the cosine function.

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x = (8.3 cm) cos[2πt...

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Question 32

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An object is undergoing simple harmonic motion of amplitude 2.3 m. If the maximum velocity of the object is 10 m/s, what is the object's angular frequency?

A) 4.3 rad/s
B) 4.8 rad/s
C) 3.5 rad/s
D) 4.0 rad/s

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Question 33

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A geologist suspends a 0.30-kg stone on an ideal spring. In equilibrium the stone stretches the spring 2.0 cm downward. The stone is then pulled an additional distance of 1.0 cm down and released from rest. (a) Write down the equation for the vertical position y of the stone as a function of time t, using the cosine function. Take the origin at the equilibrium point of the stone, with the positive y direction upward. (b) How fast is the stone moving at a time equal to 1/3 of its period of motion?

A 3.7-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant) is $450 \mathrm {~N} / \mathrm { m }$ The block is pulled from its equilibrium position at x = 0.000 m to a position x = +0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x-axis. The maximum elastic potential energy of the system is closest to

The position of an object that is oscillating on a spring is given by the equation x = (17.4 cm) cos[(5.46 s^-1) t]. What is the angular frequency for this motion?

A thin hoop is supported in a vertical plane by a nail. What should the radius of the hoop be in order for it to have a period of oscillation of 1.00 s? The moment of inertia of a hoop of mass M and radius R about a point on its rim is 2MR².

An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its elastic potential energy is a maximum?

A mass on a spring undergoes SHM. When the mass is at its maximum distance from the equilibrium position, which of the following statements about it are true? (There could be more than one correct choice.)

If a floating log is seen to bob up and down 15 times in 1.0 min as waves pass by you, what are the frequency and period of the wave?

A 34-kg child on an 18-kg swing set swings back and forth through small angles. If the length of the very light supporting cables for the swing is $4.9 \mathrm {~m}$ how long does it take for each complete back-and-forth swing? Assume that the child and swing set are very small compared to the length of the cables.

The total mechanical energy of a simple harmonic oscillating system is

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 would the period of the pendulum change if the supporting chain were to break, putting the elevator into freefall?

An object attached to an ideal spring oscillates with an angular frequency of 2.81 rad/s. The object has a maximum displacement at t = 0.00 s of 0.232 m. If the force constant (spring constant) is $29.8 \mathrm {~N} / \mathrm { m }$ what is the potential energy stored in the mass-spring system when t = 1.42 s?

In 1851 Jean Bernard Leon Foucault demonstrated the rotation of the earth using a pendulum 11.0 m long, which was set up in the Paris Observatory. How long would it have taken for Foucault's pendulum to make one complete swing back to its starting point if g = 9.81 m/s² at the observatory?

A leaky faucet drips 40 times in $30.0 \mathrm {~s}$ What is the frequency of the dripping?

A 0.50-kg object is attached to an ideal spring of spring constant (force constant) 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. What are (a) the total energy and (b) the amplitude of vibration of the system?

An object attached to an ideal spring executes simple harmonic motion. If you want to double its total energy, you could

A point on the string of a violin moves up and down in simple harmonic motion with an amplitude of 1.24 mm and a frequency of 875 Hz. (a) What is the maximum speed of that point in SI units? (b) What is the maximum acceleration of the point in SI units?

A simple pendulum that consists of a small ball of mass m and a massless wire of length L swings with a period T. Suppose now that the mass is rearranged so that mass of the ball was reduced but the mass of the wire was increased, with the total mass remaining m and the length being L. What is true about the new period of swing? (There could be more than one correct choice.)

A 0.39-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant) is $570 \mathrm {~N} / \mathrm { m } .$ The block is pulled from its equilibrium position at x = 0.000 m to a displacement x = +0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x-axis. When the position of the block is $x = 0.057 \mathrm {~m}$ its kinetic energy is closest to