Exam 20: Vibrational Motion

The figure shows a graph of the position x as a function of time t for a system undergoing simple harmonic motion.Which one of the following graphs represents the velocity of this system as a function of time? a) b) c) d)

An object attached to a spring undergoes SHM.When the object is at its maximum distance from the equilibrium position,which of the following statements are true? (There could be more than one correct choice.)

A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27 cm and a frequency of 2.55 Hz.What are the (a)maximum speed and (b)maximum acceleration of the tip of the needle?

The position of an air-track cart that is oscillating on a spring is given by the equation x = (12.4 cm)cos[(6.35 s^-1)t].At what value of t after t = 0.00 s is the cart first located at x = 8.47 cm?

A object on a spring undergoes SHM.When the object passes through the equilibrium position,which of the following statements about object-spring system are true? (There could be more than one correct choice.)

A point on the string of a violin moves up and down in simple harmonic motion with an amplitude of 1.24 mm and a frequency of 875 Hz. (a)What is the maximum speed of that point in SI units? (b)What is the maximum acceleration of the point in SI units?

A pendulum of length L is suspended from the ceiling of an elevator.When the elevator is at rest the period of the pendulum is T.How does the period of the pendulum change when the elevator moves upward with constant acceleration?

A leaky faucet drips 40 times in $30.0 \mathrm {~s} .$ What is the frequency of the dripping?

What is the length of a simple pendulum with a period of 2.0 s?

In simple harmonic motion,when is the speed the greatest? (There could be more than one correct choice.)

A package is oscillating on a spring scale with a period of 4.60 s.At time t = 0.00 s the package has zero speed and is at x = 8.30 cm.At what time after t = 0.00 s will the package first be at x = 4.15 cm?

A simple pendulum and an object oscillating on an ideal spring both have period T in an elevator at rest.If the elevator now moves downward at a uniform 2 m/s,what is true about the periods of these two systems?

If the frequency of the motion of a simple harmonic oscillator is doubled,by what factor does the maximum speed of the oscillator change?

A geologist suspends a 0.30-kg stone on an ideal spring.In equilibrium the stone stretches the spring 2.0 cm downward.The stone is then pulled an additional distance of 1.0 cm down and released from rest. (a)Write down the equation for the vertical position y of the stone as a function of time t,using the cosine function.Take the origin at the equilibrium point of the stone,with the positive y direction upward. (b)How fast is the stone moving at a time equal to 1/3 of its period of motion?

The equation of motion of a particle undergoing simple harmonic motion in the y direction is y = (2.0 cm)sin(0.60 s^-1 t).At time t = 0.60 s determine the particle's (a)position,(b)velocity,and (c)acceleration.

An astronaut has landed on Planet N-40 and conducts an experiment to determine the free fall acceleration on that planet.She uses a simple pendulum that is 0.640 m long and measures that 10 complete oscillations 26.0 s.What is the free fall acceleration on Planet N-40?

An object is attached to a vertical spring and bobs up and down between points A and B.Where is the object located when the elastic potential energy of the system object-spring is a maximum?

The quartz crystal in a digital watch has a frequency of 32.8 kHz.What is its period of oscillation?

An object is attached to a vertical spring and bobs up and down between points A and B.Where is the object located when its kinetic energy is a minimum?

The figure shows a graph of the position x as a function of time t for a system undergoing simple harmonic motion.Which one of the following graphs represents the acceleration of this system as a function of time? a) b) c) d)