Exam 14: Oscillations

A Christmas ornament made from a thin hollow glass sphere hangs from a small hook at its surface. It is observed to oscillate with a frequency of 2.50 Hz in a city where g = 9.80 m/s². What is the radius of the ornament? The moment of inertia of a hollow sphere of mass M and radius R about a point on its edge is 5MR²/3.

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?

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 kinetic energy is a maximum?

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

On the Moon, the acceleration of gravity is g/6. If a pendulum has a period T on Earth, what will its period be on the Moon?

If your heart is beating at 76.0 beats per minute, what is the frequency of your heart's oscillations in hertz?

A ball vibrates back and forth from the free end of an ideal spring having a force constant (spring constant) of 20 N/m. If the amplitude of this motion is 0.30 m, what is the kinetic energy of the ball when it is 0.30 m from its equilibrium position?

The position of an air-track cart that is oscillating on a spring is given by the equation x = (12.4 cm) cos[(6.35 s^-1)t]. At what value of t after t = 0.00 s is the cart first located at x = 8.47 cm?

A spaceship captain lands on an unknown planet. Before venturing forth, he needs to find out the acceleration due to gravity on that planet. All he has available to him is some thin light string, a stopwatch, and a small 2.75-kg metal ball (it was a rough landing). So he lets the ball swing from a 1.5-m length of the string, starting at rest, and measures that it takes 1.9 s for it to swing from the place where he released it to the place where it first stops as it reverses direction. What is the acceleration due to gravity on this planet?

The position of an object that is oscillating on an ideal 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 using the cosine function.

The figure shows a graph of the velocity v 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 simple pendulum having a bob of mass M has a period T. If you double M but change nothing else, what would be the new period?

When a certain simple pendulum is set swinging, its angular displacement θ as a function of time t obeys the equation θ = 8.5° cos(2.4 s^-1t). How long is the pendulum?

A 3.42-kg stone hanging vertically from an ideal spring on the earth undergoes simple harmonic motion at a place where g = 9.80 m/s². If the force constant (spring constant) of the spring is $12 \mathrm {~N} / \mathrm { m }$ find the period of oscillation of this setup on a planet where g = 1.60 m/s².

A guitar string is set into vibration with a frequency of 512 Hz. How many oscillations does it undergo each minute?

An air-track cart is attached to a spring and completes one oscillation every 5.67 s in simple harmonic motion. At time t = 0.00 s the cart is released at the position x = +0.250 m. What is the position of the cart when t = 29.6 s?

A ball is attached to an ideal spring and oscillates with a period T. If the mass of the ball is doubled, what is the new period?

A block attached to an ideal spring of force constant (spring constant) 15 N/m executes simple harmonic motion on a frictionless horizontal surface. At time t = 0 s, the block has a displacement of -0.90 m, a velocity of -0.80 m/s, and an acceleration of +2.9 m/s² . The mass of the block is closest to

As shown in the figure, a 0.23-kg ball is suspended from a string 6.87 m long and is pulled slightly to the left. As the ball swings through the lowest part of its motion it encounters a spring attached to the wall. The spring pushes against the ball and eventually the ball is returned to its original starting position. Find the time for one complete cycle of this motion if the spring constant (force constant) is $19 \mathrm {~N} / \mathrm { m }$ (Assume that once the pendulum ball hits the spring there is no effect due to the vertical movement of the ball.)

How much mass should be attached to a vertical ideal spring having a spring constant (force constant) of 39.5 N/m so that it will oscillate at 1.00 Hz?