Exam 14: Oscillations

An object of mass m = 8.0 kg is attached to an ideal spring and allowed to hang in the earth's gravitational field. The spring stretches $2.2 \mathrm {~cm}$ before it reaches its equilibrium position. If it were now allowed to oscillate by this spring, what would be its frequency?

Two simple pendulums, A and B, are each 3.0 m long, and the period of pendulum A is T. Pendulum A is twice as heavy as pendulum B. What is the period of pendulum B?

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

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

A package is oscillating on a spring scale with a period of 4.60 s. At time t = 0.00 s the package has zero speed and is at x = 8.30 cm. At what time after t = 0.00 s will the package first be at x = 4.15 cm?

If we double the frequency of a system undergoing simple harmonic motion, which of the following statements about that system are true? (There could be more than one correct choice.)

If both the mass of a simple pendulum and its length are doubled, the period will

A simple pendulum takes 2.00 s to make one compete swing. If we now triple the length, how long will it take for one complete swing?

A 0.250-kg stone is attached to an ideal spring and undergoes simple harmonic oscillations with a period of 0.640 s. What is the force constant (spring constant) of the spring?

Grandfather clocks are designed so they can be adjusted by moving the weight at the bottom of the pendulum up or down. Suppose you have a grandfather clock at home that runs fast. Which of the following adjustments of the weight would make it more accurate? (There could be more than one correct choice.)

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 velocity?

A 0.150-kg air track cart is attached to an ideal spring with a force constant (spring constant) of 3.58 N/m and undergoes simple harmonic oscillations. What is the period of the oscillations?

An object is oscillating on a spring with a period of 4.60 s. At time t = 0.00 s the object has zero speed and is at x = 8.30 cm. What is the acceleration of the object at t = 2.50 s?

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 minimum?

A 51.8-kg bungee jumper jumps off a bridge and undergoes simple harmonic motion. If the period of oscillation is 11.2 s, what is the spring constant (force constant) of the bungee cord?

The position of a cart that is oscillating on a spring is given by the equation x = (12.3 cm) cos[(1.26 s^-1)t]. When t = 0.805 s, what are the (a) velocity and (b) acceleration of the cart?

A 1.15-kg beaker (including its contents) is placed on a vertical spring scale. When the system is sent into vertical vibrations, it obeys the equation y = (2.3 cm)cos(17.4 s^-1 t). What is the force constant (spring constant) of the spring scale, assuming it to be ideal?

An astronaut has landed on an asteroid and conducts an experiment to determine the acceleration of gravity on that asteroid. He uses a simple pendulum that has a period of oscillation of 2.00 s on Earth and finds that on the asteroid the period is 11.3 s. What is the acceleration of gravity on that asteroid?

A 0.16-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant) is 360 N/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. When the position is x = -0.037 m, what is the acceleration of the block?

A simple pendulum has a period T on Earth. If it were used on Planet X, where the acceleration due to gravity is 3 times what it is on Earth, what would its period be?