Question 1

A block of mass $$m is $$attached to a spring with force constant $$k$$ and oscillates on a frictionless surface. If the amplitude of oscillation is doubled, what happens to the total mechanical energy of the system?

Accepted Answer

It quadruples.

Question 2

A 2.45 N object is attached to a massless spring and oscillates with a period of $$0.64 s. $$What is the spring constant $$k of $$the spring? (Use $$g = 9.8 m/s$^2)$$

Accepted Answer

$$k = 59.7 N/m$$

Question 3

Which of the following best describes the restoring force in simple harmonic motion for a spring-mass system?

Accepted Answer

$$F = -kx$$

Question 4

A simple pendulum has a length $$L$$ and period $$T on $$Earth. If the same pendulum is taken to a planet where the acceleration due to gravity is $$g'$$, what is the new period $$T'$$?

Accepted Answer

$$T' = T \sqrt{\frac{g}{g'}}$$

Question 5

For a mass-spring system in SHM, which of the following expressions gives the angular frequency?

Accepted Answer

$$\omega = \sqrt{\frac{k}{m}}$$

Question 6

A mass is attached to a vertical spring and oscillates up and down in simple harmonic motion. If the mass is moving upward and has just passed the equilibrium point, what are the signs of its velocity and acceleration (taking upward as positive)?

Accepted Answer

Velocity is positive, acceleration is negative.

Question 7

A simple pendulum on Earth has a period of $$1.75 s. On $$Planet X, its period is $$2.14 s. $$What is the acceleration due to gravity on Planet X?

Accepted Answer

$$6.55 m/s$^2$$

Question 8

Which of the following statements about the phase angle $$\phi in $$the equation $$x = A \cos(\omega t + \phi) is $$correct?

Accepted Answer

Increasing $$\phi$$ shifts the displacement vs. time graph to the left.

Question 9

A mass $$m$$ attached to a spring with force constant $$k$$ oscillates with amplitude $$A. $$What is the maximum speed of the mass during its motion?

Accepted Answer

$$v_{max} = A \sqrt{\frac{k}{m}}$$

Question 10

Which of the following is true about the energy in a simple harmonic oscillator (ignoring friction)?

Accepted Answer

The total mechanical energy is constant.

Question 11

A mass of $$8 kg is $$attached to a spring and stretches $$3.6 cm $$before reaching equilibrium. What is the spring constant $$k$$? (Use $$g = 9.8 m/s$^2)$$

Accepted Answer

$$k = 2178 N/m$$

Question 12

For a simple pendulum of length $$L$$ and small amplitude, which equation gives the period $$T$$?

Accepted Answer

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

Question 13

A block attached to a spring oscillates with period $$T. If $$the mass of the block is quadrupled, what happens to the period?

Accepted Answer

It doubles.

Question 14

Which of the following best describes the relationship between frequency $$f$$ and period $$T$$ for any periodic motion?

Accepted Answer

$$f = \frac{1}{T}$$

Question 15

A child on a swing (modeled as a simple pendulum) increases the amplitude of her swing. What happens to the period of the swing?

Accepted Answer

It remains nearly the same for small amplitudes.

Question 16

Which of the following is a necessary condition for an object to undergo simple harmonic motion?

Accepted Answer

The restoring force must be directly proportional to displacement and directed toward equilibrium.

Question 17

A mass-spring system oscillates with frequency $$f. If $$the spring constant $$k is $$increased by a factor of 4, what happens to the frequency?

Accepted Answer

It doubles.

Question 18

At which point in a mass-spring system is the potential energy of the system maximum?

Accepted Answer

At the maximum displacement (amplitude).

Question 19

Which of the following is the correct expression for the displacement as a function of time in simple harmonic motion?

Accepted Answer

$$x = A \cos(\omega t + \phi)$$

Simple Harmonic Motion and the Simple Pendulum

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