Q: A physical pendulum (lower leg) of mass $$5.0\ \text{kg}$$ and center of gravity $$18\ \text{cm}$$ from the knee swings with a frequency of $$1.6\ \text{Hz}. $$What is its moment of inertia?

$$I = 8.7 \times 10$$^{-3}$$\ \text{kg}\cdot\text{m}^2$$

Question 1

A mass hanging from a spring undergoes vertical simple harmonic motion. At which point in its motion is the magnitude of the net force equal to zero?

Accepted Answer

As the mass passes through the new, weighted equilibrium point

Question 2

For a block oscillating on a spring, if the amplitude of oscillation is doubled, what happens to the maximum kinetic energy?

Accepted Answer

It increases by a factor of four

Question 3

Given the equation for the position of an oscillating mass: $$x(t) = (2.0\ 	ext{cm}) \cos(10t)$$, what is the period of oscillation?

Accepted Answer

$$T = 0.63\ 	ext{s}$$

Question 4

An air-track glider attached to a spring oscillates with a period of $$2.0\ 	ext{s}$$ and a maximum speed of $$0.40\ 	ext{m/s}. $$What is the amplitude of the oscillation?

Accepted Answer

$$A = 0.13\ 	ext{m}$$

Question 5

A pendulum on the moon (where $$g = 1.62\ 	ext{m/s}^2) is to $$have the same period as a $$2.00\ 	ext{m}$$ pendulum on Earth ($$g = 9.8\ 	ext{m/s}^2). $$What should its length be?

Accepted Answer

$$L = 0.33\ 	ext{m}$$

Question 6

A 50 g mass oscillates according to $$x(t) = (2.0\ 	ext{cm}) \cos(10t). $$What is the spring constant $$k$$?

Accepted Answer

$$k = 5.0\ 	ext{N/m}$$

Question 7

A spring with an unstretched length of $$12\ 	ext{cm}$$ stretches by $$4.0\ 	ext{cm}$$ when an $$80\ 	ext{g}$$ ball is hung from it. What is the spring constant?

Accepted Answer

$$k = 20\ 	ext{N/m}$$

Question 8

The maximum acceleration of a hummingbird's wing tip is $$990\ 	ext{m/s}^2. $$What is this acceleration in units of $$g$$?

Accepted Answer

$$100\ g$$

Question 9

A block oscillating on a spring has a maximum kinetic energy of $$2.0\ 	ext{J}. If $$the amplitude is doubled, what is the new maximum kinetic energy?

Accepted Answer

$$8.0\ 	ext{J}$$

Question 10

A physical pendulum (lower leg) of mass $$5.0\ 	ext{kg}$$ and center of gravity $$18\ 	ext{cm}$$ from the knee swings with a frequency of $$1.6\ 	ext{Hz}. $$What is its moment of inertia?

Accepted Answer

$$I = 8.7 	imes 10$$^{-3}$$\ 	ext{kg}\cdot	ext{m}^2$$

Question 11

For the graph in the first image, what is the amplitude $$A$$ and period $$T of $$the oscillation?

Accepted Answer

Question 12

For the graph in the second image, what is the frequency $$f of $$the oscillation?

Accepted Answer

$$f = 2.0\ 	ext{Hz}$$

Question 13

A spring-mass system oscillates with period $$T$$ and amplitude $$A. $$What is the equation for its maximum speed $$v_{max}$$?

Accepted Answer

$$v_{max} = 2\pi A f$$

Question 14

A mass is released from rest at the maximum displacement of a spring. At what point in its motion is its velocity zero?

Accepted Answer

At the highest and lowest points of the oscillation

Question 15

The total mechanical energy $$E of a $$spring-mass oscillator is given by $$E = \frac{1}{2}kA^2$. If the spring constant k$ is doubled and amplitude A$ is halved, what happens to E$?

Accepted Answer

It is reduced to one-fourth

Question 16

A spring-mass system oscillates with period $$T = 0.40\ 	ext{s}$$ and mass $$m = 0.080\ 	ext{kg}. $$What is the spring constant $$k$$?

Accepted Answer

$$k = 20\ 	ext{N/m}$$

Question 17

A mass oscillates according to $$x(t) = A \cos(\omega t). $$What is the velocity at time $$t$$?

Accepted Answer

$$v(t) = -A \omega \sin(\omega t)$$

Question 18

A pendulum's period is given by $$T = 2\pi \sqrt{\frac{L}{g}}. If $$the length $$L is $$quadrupled, what happens to the period $$T$$?

Accepted Answer

It doubles

Step-by-Step Guidance for Oscillations and Simple Harmonic Motion (Ch14)

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