Q: A radio station broadcasts at $$100 \ \mathrm{MHz}. $$What is the period of the electromagnetic wave?

$$T = 1 \times 10$$^{-7}$$ \ \mathrm{s}$$

Question 1

A 0.5 kg mass is attached to a horizontal spring with a spring constant $$k = 200 \ \mathrm{N/m}. If $$the mass is pulled 0.1 m from equilibrium and released from rest, what is the period of oscillation?

Accepted Answer

$$T = 0.99 \ \mathrm{s}$$

Question 2

A mass oscillates on a spring with a period $$T = 2.0 \ \mathrm{s}. $$What is the frequency of the oscillation?

Accepted Answer

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

Question 3

A 100 g mass stretches a spring from 10 cm to 12 cm. What will be the length of the spring if the mass is replaced by a 200 g mass?

Accepted Answer

14 cm

Question 4

Which of the following best describes the restoring force for a mass on a spring displaced by $$x$$ from equilibrium?

Accepted Answer

$$F = -kx$$

Question 5

A pendulum of length $$L$$ swings with a small amplitude. Which equation gives the period of its oscillation?

Accepted Answer

$$T = 2\pi \sqrt{\frac{L}{g}}$$

Question 6

A mass on a spring is released from rest at its maximum displacement $$A. $$What is its velocity when it passes through the equilibrium position?

Accepted Answer

$$v = \omega A$$

Question 7

A building sways in the wind with amplitude $$A = 0.40 \ \mathrm{m}$$ and period $$T = 7.7 \ \mathrm{s}. $$What is the maximum acceleration of the top of the building?

Accepted Answer

$$a_{max} = 0.027 \ g$$

Question 8

Which of the following statements about simple harmonic motion (SHM) is correct?

Accepted Answer

The acceleration is maximum at the maximum displacement.

Question 9

A mass $$m is $$attached to a vertical spring and oscillates with period $$T. If $$the mass is doubled, what happens to the period?

Accepted Answer

It increases by a factor of $$\sqrt{2}.$$

Question 10

A radio station broadcasts at $$100 \ \mathrm{MHz}. $$What is the period of the electromagnetic wave?

Accepted Answer

$$T = 1 	imes 10$$^{-7}$$ \ \mathrm{s}$$

Question 11

Which of the following best describes resonance in an oscillating system?

Accepted Answer

The system oscillates with maximum amplitude when driven at its natural frequency.

Question 12

A mass on a spring is oscillating with amplitude $$A$$ and frequency $$f. $$What is the equation for its position as a function of time if it starts at maximum displacement?

Accepted Answer

$$x(t) = A \cos(2\pi f t)$$

Question 13

Which of the following is true about the energy in simple harmonic motion for a mass-spring system?

Accepted Answer

Total energy is constant and equals $$\frac{1}{2}kA^2$.

Question 14

A mass oscillates on a spring with period $$T = 2.0 \ \mathrm{s}. If $$the mass is pulled to the right and released, how long will it take to reach the leftmost point of its motion?

Accepted Answer

1.0 s

Question 15

Which of the following is a correct statement about the relationship between uniform circular motion and simple harmonic motion?

Accepted Answer

The projection of uniform circular motion onto one axis is simple harmonic motion.

Question 16

A pendulum is displaced by a small angle $$	heta. $$What is the restoring force acting on the mass?

Accepted Answer

$$F = -mg\sin	heta$$

Question 17

A mass $$m$$ attached to a spring oscillates with amplitude $$A$$ and angular frequency $$\omega. $$What is the maximum kinetic energy during the motion?

Accepted Answer

$$K_{max} = \frac{1}{2}m\$$omega^2$$A^2$

Question 18

If the amplitude of a mass-spring system is doubled, how does the total mechanical energy change?

Accepted Answer

It quadruples.

Question 19

Which of the following is NOT a characteristic of simple harmonic motion?

Accepted Answer

The acceleration is always constant.

Oscillations and Simple Harmonic Motion: Physics with Calculus Study Notes

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