Exam 14: Oscillations

Suppose you want to set up a simple pendulum with a period of 2.50 s. How long should it be (a) on Earth, at a location where g = 9.80 m/s²? (b) on a planet where g is 5.00 times what it is on Earth?

A simple harmonic oscillator oscillates with frequency f when its amplitude is A. If the amplitude is now doubled to 2A, what is the new frequency?

In a supermarket, you place a 22.3-N (around 5 lb) bag of oranges on a scale, and the scale starts to oscillate at 2.7 Hz. What is the force constant (spring constant) of the spring of the scale?

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. What are the (a) maximum speed and (b) maximum acceleration of the tip of the needle?

Tarzan swings back and forth on a long vine. His friend Jane notices in amazement that he makes 30 complete swings in 2.4 minutes. (a) What is the frequency (in hertz) of Tarzan's swing? (b) How long is the vine he is using?

When a 0.350-kg package is attached to a vertical spring and lowered slowly, the spring stretches 12.0 cm. The package is now displaced from its equilibrium position and undergoes simple harmonic oscillations when released. What is the period of the oscillations?

If the frequency of a system undergoing simple harmonic motion doubles, by what factor does the maximum value of acceleration change?

The figure shows a graph of the position x as a function of time t for a system undergoing simple harmonic motion. Which one of the following graphs represents the acceleration of this system as a function of time? a) b) c) d)

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

A ball swinging at the end of a massless string, as shown in the figure, undergoes simple harmonic motion. At what point (or points) is the magnitude of the instantaneous acceleration of the ball the greatest?

A 4.8-kg block attached to an ideal spring executes simple harmonic motion on a frictionless horizontal surface. At time t = 0.00 s, the block has a displacement of $- 0.90 \mathrm {~m}$ a velocity of $- 0.80 \mathrm {~m} / \mathrm { s }$ and an acceleration of $+ 2.9 \mathrm {~m} / \mathrm { s } ^ { 2 }$ The force constant (spring constant) of the spring is closest to

A 1.5-kg cart attached to an ideal spring with a force constant (spring constant) of 20 N/m oscillates on a horizontal, frictionless track. At time t = 0.00 s, the cart is released from rest at position x = 10 cm from the equilibrium position. (a) What is the frequency of the oscillations of the cart? (b) Determine the maximum speed of the cart. Where does the maximum speed occur? (c) Find the maximum acceleration of the mass. Where does the maximum acceleration occur? (d) How much total energy does this oscillating system contain? (e) Express the displacement as a function of time using a cosine function.

In simple harmonic motion, when is the speed the greatest? (There could be more than one correct choice.)

A 92-kg man climbs into a car with worn out shock absorbers, and this causes the car to drop down 4.5 cm. As he drives along he hits a bump, which starts the car oscillating at an angular frequency of 4.52 rad/s. What is the mass of the car?

A pendulum that was originally erected by Foucault at the Pantheon in Paris for the Paris Exhibition in 1851 was restored in 1995. It has a 28.0-kg sphere suspended from a 67.0-m light cable. How long would it take for the bob in this pendulum to move from the position of maximum displacement down to the equilibrium point?

The equation of motion of a particle undergoing simple harmonic motion in the y direction is y = (2.0 cm) sin(0.60 s^-1 t). At time t = 0.60 s determine the particle's (a) position, (b) velocity, and (c) acceleration.

A sewing machine needle moves in simple harmonic motion with a frequency of 2.5 Hz and an amplitude of 1.27 cm. (a) How long does it take the tip of the needle to move from the highest point to the lowest point in its travel? (b) How long does it take the needle tip to travel a total distance of 11.43 cm?

A 2.0 kg box is traveling at 5.0 m/s on a smooth horizontal surface when it collides with and sticks to a stationary 6.0 kg box. The larger box is attached to an ideal spring of force constant (spring constant) 150 N/m, as shown in the figure. Find (a) the amplitude of the resulting oscillations of this system, (b) the frequency of the oscillations and (c) the period of the oscillations.

A 0.30-kg block of wood is suspended on a spring. In equilibrium the wood stretches the spring 2.0 cm downward. The wood is then pulled an additional distance of 1.0 cm down and released from rest. (a) How long does it take the wood to make 3 complete cycles of vibration? (b) How much total mechanical energy does this system contain if we choose the total potential energy (elastic and gravitational) to be zero at the equilibrium position of the hanging block?

An object that hangs from the ceiling of a stationary elevator by an ideal spring oscillates with a period T. If the elevator accelerates upward with acceleration 2g, what will be the period of oscillation of the object?