Exam 15: Oscillatory Motion

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

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?

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 2.00 m-long 6.00 kg ladder pivoted at the top hangs down from a platform at the circus. A 42.0 kg trapeze artist climbs to a point where her center of mass is at the center of the ladder and swings at the system's natural frequency. The angular frequency (in s−¹) of the system of ladder and woman 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 center of mass. The angular frequency (in rad/s) for small oscillations is approximately

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

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?

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

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

The mat of a trampoline is held by 32 springs, each having a spring constant of 5 000 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.

The oscillation of the 2.0-kg mass on a spring is described by where x is in centimeters and t is in seconds. What is the force constant of the spring?

Exhibit 15-1 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) Use this exhibit to answer the following question(s). -Refer to Exhibit 15-1. The point at which the object has negative velocity and zero acceleration is

In the figure below, a disk (radius R = 1.0 m, mass = 2.0 kg) is suspended from a pivot a distance d = 0.25 m above its center of mass. For a circular disk, . The angular frequency (in rad/s) for small oscillations is approximately

A body oscillates with simple harmonic motion along the x axis. Its displacement varies with time according to the equation x = 5.0 sin (πt + π/3). The velocity (in m/s) of the body at t = 1.0 s is

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

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

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

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)?

The motion of a piston in an auto engine is simple harmonic. If the piston travels back and forth over a distance of 10 cm, and the piston has a mass of 1.5 kg, what is the maximum speed of the piston and the maximum force acting on the piston when the engine is running at 4 200 rpm?

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?