Exam 13: Periodic Motion

In the figure, a 0.24-kg ball is suspended from a very light string 9.79 m long and is pulled slightly to the left. As the ball swings without friction through the lowest part of its motion it encounters an ideal massless 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 of the spring is 21 N/m. (Assume that once the pendulum ball hits the spring there is no effect due to the vertical movement of the ball.)

A lightly damped harmonic oscillator, with a damping force proportional to its speed, is oscillating with an amplitude of 0.500 cm at time t = 0. When t = 8.20 s, the amplitude has died down to 0.400 cm. At what value of t will the oscillations have an amplitude of 0.250 cm?

An object is undergoing simple harmonic motion with frequency f = 9.7 Hz and an amplitude of 0.12 m. At t = 0.00 s the object is at x = 0.00 m. How long does it take the object to go from x = 0.00 m to x = 0.048 m?

A long thin uniform rod of length 1.50 m is to be suspended from a frictionless pivot located at some point along the rod so that its pendulum motion takes 3.00 s. How far from the center of the rod should the pivot be located?

The x component of the velocity of an object vibrating along the x-axis obeys the equation v_x(t) = (0.445 m/s) sin[(25.4 rad/s)t + 0.223]. (a) What is the amplitude of the motion of this object? (b) What is the maximum acceleration of the vibrating object?

An object is executing simple harmonic motion. What is true about the acceleration of this object? (There may be more than one correct choice.)

A 1.5-kg mass attached to an ideal massless spring with a spring constant of 20.0 N/m oscillates on a horizontal, frictionless track. At time t = 0.00 s, the mass is released from rest at x = 10.0 cm. (That is, the spring is stretched by 10.0 cm.) (a) Find the frequency of the oscillations. (b) Determine the maximum speed of the mass. At what point in the motion does the maximum speed occur? (c) What is the maximum acceleration of the mass? At what point in the motion does the maximum acceleration occur? (d) Determine the total energy of the oscillating system. (e) Express the displacement x as a function of time t.

A frictionless simple pendulum on Earth has a period of 1.75 s. On Planet X its period is 2.14 s. What is the acceleration due to gravity on Planet X?

The simple harmonic motion of an object is described by the graph shown in the figure. What is the equation for the position x(t) of the object as a function of time t?

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

A certain frictionless simple pendulum having a length L and mass M swings with period T. If both L and M are doubled, what is the new period?

A 0.28-kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is 500 N/m. The block is pulled from its equilibrium position at x = 0.00 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 displacement is x = -0.052 m, find the acceleration of the block.

A 12.0-N object is oscillating in simple harmonic motion at the end of an ideal vertical spring. Its vertical position y as a function of time t is given by y(t) = 4.50 cm cos[(19.5 s^-1)t - π/8]. (a) What is the spring constant of the spring? (b) What is the maximum acceleration of the object? (c) What is the maximum speed that the object reaches? (d) How long does it take the object to go from its highest point to its lowest point?

A 0.25 kg ideal harmonic oscillator has a total mechanical energy of 4.0 J. If the oscillation amplitude is 20.0 cm, what is the oscillation frequency?

A 25 kg object is undergoing lightly damped harmonic oscillations. If the maximum displacement of the object from its equilibrium point drops to 1/3 its original value in 1.8 s, what is the value of the damping constant b?

A mass M is attached to an ideal massless spring. When this system is set in motion, it has a period T. What is the period if the mass is doubled to 2M?

A mass M is attached to an ideal massless spring. When this system is set in motion with amplitude A, it has a period T. What is the period if the amplitude of the motion is increased to 2A?

The position of an object that is oscillating on an ideal spring is given by the equation x = (12.3 cm) cos[(1.26s^-1)t]. At time t = 0.815 s, (a) how fast is the object moving? (b) what is the magnitude of the acceleration of the object?

The position x of an object varies with time t. For which of the following equations relating x and t is the motion of the object simple harmonic motion? (There may be more than one correct choice.)

If we double only the spring constant of a vibrating ideal mass-and-spring system, the mechanical energy of the system