Exam 15: Periodic Motion

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?

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

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 uniform meter stick is freely pivoted about the 0.20-m mark.If it is allowed to swing in a vertical plane with a small amplitude and friction,what is the frequency of its oscillations?

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 t = 0.When t = 8.20 s,the amplitude has died down to 0.400 cm.At what value of t will the oscillations have an amplitude of 0.250 cm?

A machine part is vibrating along the x-axis in simple harmonic motion with a period of 0.27 s and a range (from the maximum in one direction to the maximum in the other)of 3.0 cm.At time t = 0 it is at its central position and moving in the +x direction.What is its position when t = 55 s?

The simple harmonic motion of an object is described by the graph shown in the figure.What is the equation for the position x(t)of the object as a function of time t?

A frictionless simple pendulum on Earth has a period of 1.75 s.On Planet X its period is 2.14 s.What is the acceleration due to gravity on Planet X?