Exam 12: Oscillatory Motion

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

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?

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 weight of mass m is at rest at O when suspended from a spring,as shown.When it is pulled down and released,it oscillates between positions A and B.Which statement about the system consisting of the spring and the mass is correct?

If y = 0.02 sin (30x - 400t)(SI units),the wavelength of the wave is

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. -Refer to Exhibit 15-1.The point at which the object has negative velocity and zero acceleration is

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 0.5 R 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 $\omega$ ?

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

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 ( $\pi$ t + $\pi$ /3).The phase (in rad)of the motion at t = 2 s is

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?

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

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?

The amplitude of a system moving with simple harmonic motion is doubled.The total energy will then be

At sea level,at a latitude where $g = 9.80 \frac { \mathrm { m } } { \mathrm { s } ^ { 2 } }$ ,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?

For the wave described by $y = 0.15 \sin \left[ \frac { \pi } { 16 } ( 2 x - 64 t ) \right] \text { (SI units) }$ ,determine the first positive x coordinate where y is a maximum when t = 0.

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. -Refer to Exhibit 15-1.The point at which the object has zero velocity and positive acceleration is

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

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

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. -Refer to Exhibit 15-1.A point or points at which the object has positive velocity and zero acceleration is(are)