Question 1

A block of mass $$m is $$attached to a spring with force constant $$k$$ and oscillates in simple harmonic motion (SHM) on a frictionless surface. Which of the following equations correctly describes the position $$x(t) of $$the block if it starts at maximum displacement $$A at$$ $$t=0$$?

Accepted Answer

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

Question 2

The restoring force for a mass-spring system in SHM is given by $$F_x = -kx. $$What is the corresponding acceleration $$a_x of $$the mass?

Accepted Answer

$$a_x = -\frac{k}{m}x$$

Question 3

A pendulum of length $$L$$ oscillates with small amplitude. What is the period $$T of $$its motion?

Accepted Answer

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

Question 4

A 2.45 kg block hangs from a spring with force constant $$k = 200\ \mathrm{N/m}$$ and stretches the spring by $$0.120\ \mathrm{m}. $$What is the period of oscillation if the block is pulled down and released?

Accepted Answer

$$T = 0.70\ \mathrm{s}$$

Question 5

Which of the following best describes the energy transformation in a frictionless SHM system?

Accepted Answer

Mechanical energy is constantly exchanged between kinetic and potential forms.

Question 6

A block of mass $$4.0\ \mathrm{kg}$$ attached to a spring oscillates with amplitude $$0.50\ \mathrm{m}$$ and maximum acceleration $$20\ \mathrm{m/s^2$}. $$What is the force constant $$k of $$the spring?

Accepted Answer

$$k = 160\ \mathrm{N/m}$$

Question 7

For a mass-spring system in SHM, what is the expression for the maximum speed $$v_{max} of $$the mass?

Accepted Answer

$$v_{max} = \omega A$$

Question 8

A block attached to two identical springs (each with spring constant $$k) on a $$frictionless surface oscillates as shown. What is the effective spring constant for the system?

Accepted Answer

$$k_{eff} = 2k$$

Question 9

A block of mass $$m$$ oscillates with amplitude $$A on a $$spring with force constant $$k. $$What is the total mechanical energy $$E of $$the system?

Accepted Answer

$$E = \frac{1}{2}kA^2$

Question 10

A pendulum on the Moon (where $$g_{moon} \u003c g_{earth}) $$has the same length as on Earth. How does its period compare to that on Earth?

Accepted Answer

The period is longer on the Moon.

Question 11

Which of the following is the correct formula for the angular frequency $$\omega of a $$mass-spring system?

Accepted Answer

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

Question 12

A block oscillates in SHM with amplitude $$A$$ and is at position $$x at $$some instant. What is the speed $$v_x at $$this position?

Accepted Answer

$$v_x = \pm \sqrt{\frac{k}{m}(A^2$ - x^2$)}$$

Question 13

Which of the following statements about simple harmonic motion is FALSE?

Accepted Answer

The frequency depends on the amplitude.

Question 14

A mass-spring system oscillates with frequency $$f. If $$the mass is doubled, what happens to the frequency?

Accepted Answer

The frequency decreases by a factor of $$\sqrt{2}.$$

Question 15

A block of mass $$0.245\ \mathrm{kg} is $$attached to two identical springs, each with $$k = 7580\ \mathrm{N/m}$$, on a frictionless floor. What is the frequency of oscillation?

Accepted Answer

$$f = 40.0\ \mathrm{Hz}$$

Question 16

Which of the following best explains why the small-angle approximation $$\sin	heta \approx 	heta is $$used for pendulums in SHM?

Accepted Answer

It simplifies the equation of motion to a linear differential equation.

Question 17

A mass-spring system is oscillating with amplitude $$A$$ and period $$T. At $$what position is the kinetic energy of the mass maximum?

Accepted Answer

At $$x = 0 ($$the equilibrium position)

Chapter 11: Periodic Motion and Simple Harmonic Motion

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