Question 1

The amplitude of a lightly damped harmonic oscillator decreases from 60.0 cm to 40.0 cm in 10.0 s. What will be the amplitude of the harmonic oscillator after another 10.0 s passes?

Accepted Answer

The amplitude of a lightly damped harmonic oscillator decreases exponentially over time. Given that the amplitude decreases from 60.0 cm to 40.0 cm in 10.0 s, it means that after another 10.0 s, the amplitude will decrease by the same factor, which is 40.0/60.0 = 2/3. Therefore, after another 10.0 s, the amplitude will be 2/3 of 40.0 cm, which is approximately 26.7 cm.

Question 2

An ideal massless spring with a spring constant of 2.00 N/m is attached to an object of 75.0 g.The system has a small amount of damping.If the amplitude of the oscillations decreases from 10.0 mm to 5.00 mm in 15.0 s,what is the magnitude of the damping constant b?

Accepted Answer

The answer of An ideal massless spring with a spring...

Question 3

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?

Accepted Answer

The frequency of oscillations of a simple pendulum is given by:
$$f=\frac{1}{2\pi}\sqrt{\frac{g}{l}}$$
where $g$ is the acceleration due to gravity and $l$ is the length of the pendulum. In this case, the pivot point is at the 0.20-m mark, so the effective length of the pendulum is 0.80 m (from the pivot point to the end of the meter stick). Thus:
$$f=\frac{1}{2\pi}\sqrt{\frac{9.8\,	ext{m/s}^2}{0.80\,	ext{m}}} \approx 0.66\,	ext{Hz}$$
Therefore, the best choice is B.

Question 4

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?

Accepted Answer

The answer of A lightly damped harmonic oscillator,with a damping...

Question 5

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.

Accepted Answer

The answer of A 5.0-kg block is attached to an...

Question 6

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?

Accepted Answer

The answer of A long thin uniform rod of length...

Question 7

A large stick is pivoted about one end and allowed to swing back and forth with no friction as a physical pendulum.The mass of the stick is 5.40 kg and its center of gravity (found by finding its balance point)is 1.80 m from the pivot.If the period of the swinging stick is 6.90 seconds,what is the moment of inertia of the stick about an axis through the pivot?

Accepted Answer

The answer of A large stick is pivoted about one...

Question 8

A 2.15 kg lightly damped harmonic oscillator has an angular oscillation frequency of 0.261 rad/s.If the maximum displacement of 2.0 m 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?

Accepted Answer

The answer of A 2.15 kg lightly damped harmonic oscillator...

Question 9

A 25 kg object is undergoing lightly damped harmonic oscillations.If the maximum displacement of the object from its equilibrium point drops to 1/3 its original value in 1.8 s,what is the value of the damping constant b?

Accepted Answer

The answer of A 25 kg object is undergoing lightly...

Quiz 15: Periodic Motion