Exam 16: Oscillatory Motion

An object of mass m is attached to string of length L. When it is released from point A, the object oscillates between points A and B. Which statement about the system consisting of the pendulum and the Earth is correct?

Two circus clowns (each having a mass of 50 kg) swing on two flying trapezes (negligible mass, length 25 m) shown in the figure. At the peak of the swing, one grabs the other, and the two swing back to one platform. The time for the forward and return motion is:

Refer to Exhibit 16-1 below.Exhibit 16-1 A graph of position versus time for an object oscillating at the free end of a horizontal spring is shown below. The point at which the object has zero velocity and positive acceleration is:

A torsional pendulum consists of a solid disk (mass = 2.0 kg, radius = 1.0 m) suspended by a wire attached to a rigid support. The body oscillates about the support wire. If the torsion constant is 16 N.m/rad, what is the angular frequency (in rad/s)?

Refer to Exhibit 16-1 below.Exhibit 16-1 A graph of position versus time for an object oscillating at the free end of a horizontal spring is shown below. A point or points at which the object has positive velocity and zero acceleration is(are):

Which of the following combinations of variables results in the greatest period for a pendulum?

A body of mass 5.0 kg is suspended by a spring, which stretches 10 cm when the mass is attached. It is then displaced downward an additional 5.0 cm and released. Its position as a function of time is approximately:

The mat of a trampoline is held by 32 springs, each having a spring constant of 5000 N/m. A person with a mass of 40.0 kg jumps from a platform 1.93 m high onto the trampoline. Determine the stretch of each of the springs.

To double the total energy of a mass oscillating at the end of a spring with amplitude A, we need to:

The mass in the figure below slides on a frictionless surface. When the mass is pulled out, spring 1 is stretched a distance x1 from its equilibrium position and spring 2 is stretched a distance x2. The spring constants are k1 and k2 respectively. The force pulling back on the mass is:

The figure shows a uniform rod (length L = 1.0 m, mass = 2.0 kg) suspended from a pivot a distance d = 0.25 m above its centre of mass. The angular frequency (in rad/s) for small oscillations is approximately:

John says that the value of the function cos[ $\omega$ (t + T) + $\varphi$ ], obtained one period T after time t, is greater than cos( $\omega$ t + $\varphi$ ) by 2 $\pi$ . Larry says that it is greater by the addition of 1.00 to cos( $\omega$ t + $\varphi$ ). Which one, if either, is correct?

Three pendulums with strings of the same length and bobs of the same mass are pulled out to angles $\theta$ 1, $\theta$ 2 and $\theta$ 3 respectively and released. The approximation sin $\theta$ = $\theta$ holds for all three angles, with $\omega$ 3 > $\omega$ 2 > $\omega$ 1. How do the angular frequencies of the three pendulums compare?

Simple harmonic oscillations can be modelled by the projection of circular motion at constant angular velocity onto a diameter of the circle. When this is done, the analogue along the diameter of the acceleration of the particle executing simple harmonic motion is:

In an inertia balance, a body supported against gravity executes simple harmonic oscillations in a horizontal plane under the action of a set of springs. If a 1.00 kg body vibrates at 1.00 Hz, a 2.00 kg body will vibrate at:

A damped oscillator is released from rest with an initial displacement of 10.00 cm. At the end of the first complete oscillation the displacement reaches 9.05 cm. When 4 more oscillations are completed, what is the displacement reached?

When a damping force is applied to a simple harmonic oscillator which has angular frequency $\omega$ 0 in the absence of damping, the new angular frequency $\omega$ is such that:

The motion of a particle connected to a spring is described by x = 10 sin ( $\pi$ t). At what time (in s) is the potential energy equal to the kinetic energy?

Refer to Exhibit 16-1 below.Exhibit 16-1 A graph of position versus time for an object oscillating at the free end of a horizontal spring is shown below. The point at which the object has negative velocity and zero acceleration is:

An archer pulls her bow string back 0.40 m by exerting a force that increases uniformly from zero to 240 N. What is the equivalent spring constant of the bow, and how much work is done in pulling the bow?