Q: A vertical spring stretches by $$0.1 m $$when a $$2 kg $$mass is attached. What is the force constant $$k of $$the spring?

$$k = \frac{2 \times 9.8}{0.1} = 196 N/m$$

Question 1

A mass $$m is $$attached to an ideal spring with force constant $$k$$ and set into simple harmonic motion (SHM) with amplitude $$A. $$Which of the following changes will increase the period $$T of $$oscillation?

Accepted Answer

Increasing the mass $$m$$ while keeping $$k$$ and $$A$$ constant.

Question 2

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

Accepted Answer

$$F_x = -kx$$

Question 3

A pendulum clock is taken from Earth to the Moon, where the acceleration due to gravity is about $$1/6$$ that on Earth. How does the period $$T of $$the pendulum change?

Accepted Answer

The period increases by a factor of $$\sqrt{6}.$$

Question 4

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

Accepted Answer

The potential energy is maximum at the amplitude.

Question 5

A $$0.5 kg $$mass oscillates on a spring with force constant $$k = 200 N/m. $$What is the angular frequency $$\omega of $$the motion?

Accepted Answer

$$\omega = \sqrt{\frac{200}{0.5}} = 20$$ rad/s

Question 6

Which of the following best explains why the amplitude of a real-world oscillator decreases over time?

Accepted Answer

Dissipative forces such as friction cause damping.

Question 7

A child on a swing (modeled as a simple pendulum) is pushed periodically at the same frequency as the swing's natural frequency. What phenomenon is observed?

Accepted Answer

Resonance

Question 8

For a mass-spring system in SHM, which of the following equations gives the displacement as a function of time?

Accepted Answer

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

Question 9

A vertical spring stretches by $$0.1 m $$when a $$2 kg $$mass is attached. What is the force constant $$k of $$the spring?

Accepted Answer

$$k = \frac{2 	imes 9.8}{0.1} = 196 N/m$$

Question 10

Which of the following is true for the velocity $$v_x$$ and acceleration $$a_x in $$SHM described by $$x(t) = A \cos(\omega t + \phi)$$?

Accepted Answer

$$v_x is $$maximum when $$x = 0$$ and $$a_x is $$maximum when $$x = \pm A$$

Question 11

A physical pendulum and a simple pendulum both have the same period. If the mass distribution of the physical pendulum is changed so that its moment of inertia increases, what happens to its period?

Accepted Answer

The period increases.

Question 12

Which of the following best describes the effect of increasing the amplitude $$A in a $$mass-spring SHM system (with $$m$$ and $$k$$ constant)?

Accepted Answer

The period remains unchanged.

Question 13

A molecule can be modeled as two atoms connected by a spring. Near equilibrium, the potential energy curve is approximately a parabola. What does this imply about the motion of the atoms for small displacements?

Accepted Answer

The atoms undergo simple harmonic motion.

Question 14

A damped oscillator is subject to a periodic driving force. At which driving frequency does the amplitude of oscillation become maximum?

Accepted Answer

At the natural frequency of the undamped oscillator.

Question 15

Which of the following is the correct expression for the total mechanical energy $$E of a $$mass-spring system in SHM with amplitude $$A$$?

Accepted Answer

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

Question 16

A coil spring exerts a restoring torque $$	au = -\kappa 	heta on a $$balance wheel. What type of motion results?

Accepted Answer

Angular simple harmonic motion

Question 17

A mass-spring system is oscillating with amplitude $$A. At $$what displacement $$x is $$the energy equally divided between kinetic and potential energy?

Accepted Answer

$$x = \pm \frac{A}{\sqrt{2}}$$

Question 18

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

Accepted Answer

The acceleration is always in the direction of velocity.

Question 19

A lady beetle's wings oscillate due to a periodic driving force from its muscles. The frequency of the wing oscillation is:

Accepted Answer

Equal to the frequency of the driving force.

Chapter 14: Periodic Motion – Study Notes

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