Question 1

A child and an adult are on adjacent swings of equal length at a playground. If both start swinging at the same time, which of the following statements is correct about their motion?

Accepted Answer

Both will swing with the same period because the period of a simple pendulum depends only on the length of the swing.

Question 2

A 0.250-kg mass on a spring has a velocity given by $$v(t) = (4.70\ \mathrm{cm/s}) \cos[(4.16\ \mathrm{rad/s}) t]. $$What is the period of the oscillation?

Accepted Answer

$$T = 1.51\ \mathrm{s}$$

Question 3

Which of the following best describes the energy transformation in a frictionless spring-cart system as it oscillates?

Accepted Answer

Potential energy is converted to kinetic energy and vice versa, with total mechanical energy remaining constant.

Question 4

A mass attached to a spring oscillates with amplitude $$A$$ and angular frequency $$\omega. $$What is the maximum acceleration of the mass?

Accepted Answer

$$a_{max} = \$$omega^2$$ A$$

Question 5

For a simple pendulum of length $$\ell$$ and small amplitude, what is the period $$T of $$oscillation?

Accepted Answer

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

Question 6

A 5.0-kg cart is attached to a horizontal spring with spring constant $$k = 75\ \mathrm{N/m}. If $$the cart is released from rest at $$x = 0.32\ \mathrm{m}$$, what is the amplitude of oscillation?

Accepted Answer

$$A = 0.50\ \mathrm{m}$$

Question 7

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

Accepted Answer

The amplitude of the angular displacement must be much less than 1 radian.

Question 8

A mass-spring system oscillates with period $$T. If $$the mass is doubled and the spring constant remains the same, what happens to the period?

Accepted Answer

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

Question 9

A pendulum clock is designed so that the time between a 'tick' and a 'tock' is $$0.5\ \mathrm{s}. $$What should the length of the pendulum be? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\ell = 0.25\ \mathrm{m}$$

Question 10

Which type(s) of equilibrium allow(s) periodic motion?

Accepted Answer

Stable equilibrium only.

Question 11

A mass attached to a spring oscillates between $$x = -5\ \mathrm{cm}$$ and $$x = 45\ \mathrm{cm}$$, taking $$0.20\ \mathrm{s} to go $$from one extreme to the other. What is the amplitude of the motion?

Accepted Answer

$$A = 25\ \mathrm{cm}$$

Question 12

The restoring force for a simple pendulum is provided by which of the following?

Accepted Answer

The component of the gravitational force perpendicular to the string.

Question 13

If a mass-spring system is taken to the Moon, where the acceleration due to gravity is smaller than on Earth, how does the period of oscillation change?

Accepted Answer

The period remains the same because it depends only on the mass and spring constant.

Question 14

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

Accepted Answer

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

Question 15

Which of the following quantities is required, in addition to the initial position, to determine the initial phase of a simple harmonic oscillator?

Accepted Answer

The initial velocity.

Question 16

A mass-spring system oscillates with frequency $$f. $$What is the angular frequency $$\omega$$?

Accepted Answer

$$\omega = 2\pi f$$

Question 17

A ball in a bowl is displaced slightly from its equilibrium position and released. Which statement best describes its subsequent motion?

Accepted Answer

It will execute simple harmonic motion if the displacement is small.

Question 18

For a mass-spring system, which of the following will decrease the period of oscillation?

Accepted Answer

Increasing the spring constant.

Question 19

A torsion oscillator consists of a disk suspended by a fiber. For small angular displacements, the equation of motion is analogous to which of the following?

Accepted Answer

Simple harmonic motion.

Periodic Motion and Simple Harmonic Motion: Study Notes for Physics with Calculus

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