Q: A pendulum exhibits simple harmonic motion only for small angles. Which of the following is the best explanation?

For small angles, $$\sin \theta \approx \theta$$, making the restoring force proportional to displacement.

Q: A mass on a spring oscillates with $$A = 0.10 m $$and $$\omega = 5$$ rad/s. What is the maximum speed $$v_{max}$$?

$$v_{max} = 0.10 \times 5 = 0.5 m/s$$

Question 1

Which of the following best describes simple harmonic motion (SHM)?

Accepted Answer

Motion where the restoring force is proportional to the displacement and directed toward equilibrium.

Question 2

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

Accepted Answer

$$E = \frac{1}{2} k A^2$

Question 3

For a mass-spring system in SHM, which of the following equations correctly relates the angular frequency $$\omega to $$the mass $$m$$ and spring constant $$k$$?

Accepted Answer

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

Question 4

A 0.5 kg mass is attached to a spring with $$k = 200 N/m. $$What is the period $$T of $$oscillation?

Accepted Answer

$$T = 2\pi \sqrt{\frac{0.5}{200}}$$

Question 5

Which of the following is true about the velocity of an object in SHM at the equilibrium position?

Accepted Answer

The velocity is at its maximum value.

Question 6

A pendulum exhibits simple harmonic motion only for small angles. Which of the following is the best explanation?

Accepted Answer

For small angles, $$\sin 	heta \approx 	heta$$, making the restoring force proportional to displacement.

Question 7

Given the equation for position in SHM: $$x(t) = A \sin(\omega t + \phi)$$, what does $$\phi$$ represent?

Accepted Answer

The phase constant.

Question 8

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

Accepted Answer

It quadruples.

Question 9

A mass on a spring oscillates with $$A = 0.10 m $$and $$\omega = 5$$ rad/s. What is the maximum speed $$v_{max}$$?

Accepted Answer

$$v_{max} = 0.10 	imes 5 = 0.5 m/s$$

Question 10

Which of the following graphs best represents the kinetic energy (KE) and potential energy (PE) of a mass-spring system in SHM over time?

Accepted Answer

KE and PE oscillate out of phase; when one is maximum, the other is minimum.

Question 11

A mass-spring system is described by $$x(t) = 0.04 \sin(4\pi t). $$What is the frequency of oscillation?

Accepted Answer

2 Hz

Question 12

Which of the following statements about the restoring force in SHM is correct?

Accepted Answer

The restoring force is proportional to the displacement and directed toward equilibrium.

Question 13

A 2.0 kg mass oscillates on a spring with $$k = 50 N/m. $$What is the angular frequency $$\omega$$?

Accepted Answer

$$\omega = \sqrt{\frac{50}{2.0}}$$

Question 14

Which of the following is the correct expression for the acceleration $$a(t) of a $$mass in SHM?

Accepted Answer

$$a(t) = -\$$omega^2$$ x(t)$$

Question 15

A mass is released from rest at its maximum displacement in SHM. What is its velocity as it passes through equilibrium?

Accepted Answer

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

Question 16

If the frequency of a mass-spring system is 5 Hz, what is its period?

Accepted Answer

$$T = 0.2 s$$

Question 17

Which of the following is a necessary condition for a pendulum to exhibit simple harmonic motion?

Accepted Answer

The amplitude must be less than about $$15^\circ.$$

Question 18

A mass-spring system has amplitude $$A$$ and period $$T. At $$what time after passing through equilibrium will it reach its maximum displacement?

Accepted Answer

$$t = T/4$$

Question 19

Which of the following best describes the energy transformation in a mass-spring system undergoing SHM?

Accepted Answer

Potential energy is converted to kinetic energy and vice versa, with total energy conserved.

Oscillations and Simple Harmonic Motion: Study Notes

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