Question 1

A mass $$m is $$attached to an ideal spring with force constant $$k$$ and oscillates in simple harmonic motion. If the mass is doubled while keeping $$k$$ constant, what happens to the period $$T of $$oscillation?

Accepted Answer

The period $$T$$ increases by a factor of $$\sqrt{2}.$$

Question 2

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

Accepted Answer

$$F = -kx$$

Question 3

A pendulum clock is moved from Earth to the Moon, where gravity is weaker. What happens to the period of the pendulum?

Accepted Answer

The period increases.

Question 4

For a simple harmonic oscillator, which of the following equations gives the displacement $$x as a $$function of time $$t$$?

Accepted Answer

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

Question 5

A car’s suspension system can be modeled as a damped oscillator. If the damping is increased, what happens to the amplitude of oscillation after hitting a bump?

Accepted Answer

The amplitude decreases more rapidly.

Question 6

Which of the following statements about the energy in simple harmonic motion is correct?

Accepted Answer

The total mechanical energy is constant and equals $$\frac{1}{2}kA^2$.

Question 7

A child on a swing is an example of which type of pendulum?

Accepted Answer

Physical pendulum

Question 8

If the amplitude $$A of a $$simple harmonic oscillator is doubled, what happens to the period $$T$$?

Accepted Answer

The period $$T$$ remains unchanged.

Question 9

A molecule consists of two atoms separated by a distance $$r. $$Near equilibrium, the potential energy $$U(r)$$ can be approximated by:

Accepted Answer

A parabola

Question 10

Which of the following best describes resonance in a forced oscillator?

Accepted Answer

It occurs when the driving frequency matches the natural frequency, causing a large amplitude response.

Question 11

A vertical spring is compressed by a weight $$mg a $$distance $$\Delta l. $$What is the force constant $$k of $$the spring?

Accepted Answer

$$k = \frac{mg}{\Delta l}$$

Question 12

For a physical pendulum, which factor does NOT affect the period of oscillation?

Accepted Answer

The amplitude (for small angles)

Question 13

Which equation gives the angular frequency $$\omega$$ for a mass-spring system in SHM?

Accepted Answer

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

Question 14

A coil spring exerts a restoring torque $$	au_z = -k	heta. $$What is $$k$$ called in this context?

Accepted Answer

Torsion constant

Question 15

A lady beetle’s wings beat at the same frequency as the periodic driving force from its muscles. This is an example of:

Accepted Answer

Resonance

Question 16

In SHM, the velocity $$v_x as a $$function of time is given by:

Accepted Answer

$$v_x = -\omega A \sin(\omega t + \phi)$$

Question 17

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

Accepted Answer

Changing $$\phi$$ shifts the graph horizontally.

Question 18

A tuning fork with larger mass vibrates at a lower frequency. This is because:

Accepted Answer

Frequency is inversely proportional to mass.

Question 19

Which of the following best describes the relationship between frequency $$f$$ and period $$T$$?

Accepted Answer

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

Chapter 14: Periodic Motion – Study Notes

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