Q: A physical pendulum consists of a $$5.0\ \text{kg}$$ lower leg with its center of gravity $$18\ \text{cm}$$ from the knee. If its oscillation frequency is $$1.6\ \text{Hz}$$, what is its moment of inertia?

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

Question 1

A mass hanging from a spring undergoes vertical simple harmonic motion. At which point in the motion is the magnitude of the net force on the mass 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 has a period equal to that of a $$2.00\ 	ext{m}$$ pendulum on Earth. If the moon's gravity is $$1.62\ 	ext{m/s}^2$$ and Earth's is $$9.8\ 	ext{m/s}^2$$, what is the length of the pendulum on the moon?

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 has an unstretched length of $$12\ 	ext{cm}. $$When an $$80\ 	ext{g}$$ ball is hung from it, the length increases by $$4.0\ 	ext{cm}. $$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 oscillates on a spring with maximum kinetic energy $$2.0\ 	ext{J}. If $$the amplitude is tripled, what is the new maximum kinetic energy?

Accepted Answer

$$18.0\ 	ext{J}$$

Question 10

A physical pendulum consists of a $$5.0\ 	ext{kg}$$ lower leg with its center of gravity $$18\ 	ext{cm}$$ from the knee. If its oscillation frequency is $$1.6\ 	ext{Hz}$$, what is its moment of inertia?

Accepted Answer

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

Question 11

For the graph in Figure Q14.10 (first image), what is the frequency $$f of $$the oscillation?

Accepted Answer

$$f = 0.50\ 	ext{Hz}$$

Question 12

For the graph in Figure Q14.10 (first image), what is the amplitude $$A of $$the oscillation?

Accepted Answer

$$A = 40\ 	ext{mm}$$

Question 13

For the position function $$x(t) = A\cos\left(\frac{2\pi t}{T}\right)$$, what is the velocity at $$t = 0$$?

Accepted Answer

$$v(0) = 0$$

Question 14

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

Accepted Answer

$$v_{max} = \frac{2\pi A}{T}$$

Question 15

A $$0.080\ 	ext{kg}$$ ball is hung from a spring and stretches it by $$4.0\ 	ext{cm}. If $$the ball is pulled down another $$4.0\ 	ext{cm}$$ and released, what is the period of oscillation?

Accepted Answer

$$T = 0.40\ 	ext{s}$$

Question 16

For a simple harmonic oscillator, where is the acceleration greatest?

Accepted Answer

At the highest and lowest points of the oscillation

Question 17

If the maximum speed of an oscillator is $$v_{max}$$ and the period is $$T$$, what is the amplitude $$A$$?

Accepted Answer

$$A = \frac{v_{max} T}{2\pi}$$

Question 18

A mass is gently hung from a vertical spring. The spring stretches to a new equilibrium length. What is the distance below the initial unstretched position?

Accepted Answer

$$\frac{mg}{k}$$

Question 19

For the second graph (second image), what is the amplitude $$A of $$the oscillation?

Accepted Answer

$$A = 4\ 	ext{cm}$$

Oscillations: Simple Harmonic Motion, Energy, and Applications

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