Exam 14: Periodic Motion

An object of mass 6.8 kg is attached to an ideal massless spring of spring constant 1690 N/m.The object is Calculate the maximum speed the object reaches during its motion.

A 2.15 kg lightly damped harmonic oscillator has an angular oscillation frequency of .If the maximum displacement of occurs when t = 0.00 s,and the damping constant b is 0.74 kg/s what is the object's displacement when t = 4.01 s?

A frictionless pendulum released from 65 degrees with the vertical will vibrate with the same frequency as if it were released from 5 degrees with the vertical because the period is independent of the amplitude and mass.

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 simple harmonic oscillator has an amplitude of 3.50 cm and a maximum speed of 26.0 cm/s.What is its speed when the displacement is 1.75 cm?

In the figure,two masses,M = 16 kg and m = 12.8.0 kg,are connected to a very light rigid bar and are attached to an ideal massless spring of spring constant 100 N/m.The system is set into oscillation with an amplitude of 78 cm.At the instant when the acceleration is at its maximum,the 16-kg mass separates from the 12.8.0-kg mass,which then remains attached to the spring and continues to oscillate.What will be the amplitude of oscillation of the 12.8.0-kg mass?

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

A 2.0 kg block on a frictionless table is connected to two ideal massless springs with spring constants k₁ and k₂ whose opposite ends are fixed to walls,as shown in the figure.What is angular frequency of the oscillation if and

A 0.025-kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is 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 what is the kinetic energy of the block?

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?

An object that weighs 2.450 N is attached to an ideal massless spring and undergoes simple harmonic oscillations with a period of 0.640 s.What is the spring constant of the spring?

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?

A 56 kg bungee jumper jumps off a bridge and undergoes simple harmonic motion.If the period of oscillation is 11.2 s,what is the spring constant of the bungee cord,assuming it has negligible mass compared to that of the jumper?

An ideal massless spring with a spring constant of 2.00 N/m is attached to an object of .The system has a small amount of damping.If the amplitude of the oscillations decreases from to in ,what is the magnitude of the damping constant b?

A 5.0-kg block is attached to an ideal massless spring whose spring constant is 125 N/m.The block is pulled from its equilibrium position at x = 0.00 m to a position at x = +0.687 m and is released from rest.The block then executes lightly damped oscillation along the x-axis,and the damping force is proportional to the velocity.When the block first returns to x = 0.00 m,its x component of velocity is -2.0 m/s and its x component of acceleration is +5.6 m/s². (a)What is the magnitude of the acceleration of the block upon release at x = +0.687 m. (b)Find the damping constant b.

A 0.25 kg ideal harmonic oscillator has a total mechanical energy of If the oscillation amplitude is what is the oscillation frequency?

A 2.00-kg object is attached to an ideal massless horizontal spring of spring constant 100.0 N/m and is at rest on a frictionless horizontal table.The spring is aligned along the x-axis and is fixed to a peg in the table.Suddenly this mass is struck by another 2.00-kg object traveling along the x-axis at 3.00 m/s,and the two masses stick together.What are the amplitude and period of the oscillations that result from this collision?

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?

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

A machine part is vibrating along the x-axis in simple harmonic motion with a period of and a range (from the maximum in one direction to the maximum in the other)of .At time t = 0 it is at its central position and moving in the +x direction.What is its position when ?