Exam 20: Vibrational Motion

When a 0.350-kg package is attached to a vertical spring and lowered slowly,the spring stretches 12.0 cm.The package is now displaced from its equilibrium position and undergoes simple harmonic oscillations when released.What is the period of the oscillations?

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 downward with constant acceleration?

A 0.30-kg block of wood is suspended on a spring.In equilibrium the wood stretches the spring 2.0 cm downward.The wood is then pulled an additional distance of 1.0 cm down and released from rest. (a)How long does it take the wood to make 3 complete cycles of vibration? (b)How much total mechanical energy does this system contain if we choose the total potential energy (elastic and gravitational)to be zero at the equilibrium position of the hanging block?

A 2.0 kg box is traveling at 5.0 m/s on a smooth horizontal surface when it collides with and sticks to a stationary 6.0 kg box.The larger box is attached to an ideal spring of force constant (spring constant)150 N/m,as shown in the figure.Find (a)the amplitude of the resulting oscillations of this system,(b)the frequency of the oscillations and (c)the period of the oscillations.

An object of mass 6.8 kg is attached to an ideal spring of force constant (spring constant)1720 N/m.The object is set into simple harmonic motion,with an initial velocity of $v _ { \mathrm { O } } = 4.1 \mathrm {~m} / \mathrm { s }$ and an initial displacement of $x _ { 0 } = 0.11 \mathrm {~m}$ Calculate the maximum speed the object reaches during its motion.

An astronaut has landed on an asteroid and conducts an experiment to determine the free fall acceleration on that asteroid.He uses a simple pendulum that has a period of oscillation of 2.00 s on Earth and finds that on the asteroid the period is 11.3 s.What is the free fall acceleration on that asteroid?

A ball swinging at the end of a massless string,as shown in the figure,undergoes simple harmonic motion.At what point (or points)is the magnitude of the instantaneous acceleration of the ball the greatest?

A ball is attached to an ideal spring and oscillates with a period T.If the mass of the ball is doubled,what is the new period?

The position of an object that is oscillating on a spring is given by the equation x = (18.3 cm)cos[(2.35 s^-1)t].What are the (a)frequency,(b)amplitude,and (c)period of this motion?

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 velocity?

Suppose you want to set up a simple pendulum with a period of 2.50 s.How long should it be (a)on Earth,at a location where g = 9.80 m/s²? (b)on a planet where g is 5.00 times what it is on Earth?

A 0.50-kg object is attached to an ideal spring of spring constant 20 N/m along a horizontal,frictionless surface.The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position.At what distance from the equilibrium position are the kinetic energy and potential energy of the system the same?

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

An object is oscillating on a spring with a period of 4.60 s.At time t = 0.00 s the object has zero speed and is at x = 8.30 cm.What is the acceleration of the object at t = 2.50 s?

A 4.8-kg block attached to an ideal spring executes simple harmonic motion on a frictionless horizontal surface.At time t = 0.00 s,the block has a displacement of $- 0.90 \mathrm {~m}$ a velocity of $- 0.80 \mathrm {~m} / \mathrm { s } \text {, }$ and an acceleration of $+ 2.9 \mathrm {~m} / \mathrm { s } ^ { 2 }$ The spring constant of the spring is closest to

A 34-kg child on an 18-kg swing set swings back and forth through small angles.If the length of the very light supporting cables for the swing is $4.9 \mathrm {~m}$ how long does it take for each complete back-and-forth swing? Assume that the child and swing set are very small compared to the length of the cables.

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 minimum?

A sewing machine needle moves in simple harmonic motion with a frequency of 2.5 Hz and an amplitude of 1.27 cm. (a)How long does it take the tip of the needle to move from the highest point to the lowest point in its travel? (b)How long does it take the needle tip to travel a total distance of 11.43 cm?

An air-track cart is attached to a spring and completes one oscillation every 5.67 s in simple harmonic motion.At time t = 0.00 s the cart is released at the position x = +0.250 m.What is the position of the cart when t = 29.6 s?

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