Exam 16: Oscillations

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 ​ ​

The mass in the figure slides on a frictionless surface. If m = 2 kg, k1 = 800 N/m and k2 = 500 N/m, the frequency of oscillation (in Hz) is approximately ​ ​

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)?

A uniform rod (mass m = 1.0 kg and length L = 2.0 m) pivoted at one end oscillates in a vertical plane as shown below. The period of oscillation (in s) is approximately ​ ​

At sea level, at a latitude where , a pendulum that takes 2.00 s for a complete swing back and forth has a length of 0.993 m. What is the value of g in m/s² at a location where the length of such a pendulum is 0.970 m?

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

Three pendulums with strings of the same length and bobs of the same mass are pulled out to angles θ1, θ2, and θ3 respectively, and released. The approximation sin θ = θ holds for all three angles, with θ3 > θ2 > θ1. How do the angular frequencies of the three pendulums compare?

When a damping force is applied to a simple harmonic oscillator which has angular frequency ω0 in the absence of damping, the new angular frequency ω is such that

An automobile (m = 1.00 × 10³ kg) is driven into a brick wall in a safety test. The bumper behaves like a spring (k = 5.00 × 10⁶ N/m), and is observed to compress a distance of 3.16 cm as the car is brought to rest. What was the initial speed of the automobile?

In the figure below, a hoop (radius R = 1.0 m, mass = 2.0 kg) having four spokes of negligible mass is suspended from a pivot a distance d = .25 m above its center of mass. The angular frequency (in rad/s) for small oscillations is approximately ​ ​

Ellen says that whenever the acceleration is directly proportional to the displacement of an object from its equilibrium position, the motion of the object is simple harmonic motion. Mary says this is true only if the acceleration is opposite in direction to the displacement. Which one, if either, is correct?

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 hoop, a solid cylinder, and a solid sphere all have the same mass m and the same radius R. Each is mounted to oscillate about an axis a distance 0.5R from the center. The axis is perpendicular to the circular plane of the hoop and the cylinder and to an equatorial plane of the sphere as shown below. Which is the correct ranking in order of increasing angular frequency ω? ​ ​

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

A body oscillates with simple harmonic motion along the x axis. Its displacement varies with time according to the equation x = 5 sin (πt + π/3). The phase (in rad) of the motion at t = 2 s is

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?

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.

A graph of position versus time for an object oscillating at the free end of a horizontal spring is shown below. ​ ​ Use this exhibit to answer the following question(s). -The point at which the object has zero velocity and negative acceleration is

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 ​ ​ ​

A graph of position versus time for an object oscillating at the free end of a horizontal spring is shown below. ​ ​ Use this exhibit to answer the following question(s). -A point or points at which the object has positive velocity and zero acceleration is(are)