$$\$$phi_0$$ = -\tan$$^{-1}$$\left(\frac{v_i}{\omega x_i}\right)$$

Question 1

Which of the following best describes the period $$T of a $$harmonic oscillator with angular frequency $$\omega$$?

Accepted Answer

$$T = \frac{2\pi}{\omega}$$

Question 2

A mass $$m$$ attached to a spring with spring constant $$k$$ oscillates horizontally. What is the expression for its angular frequency $$\omega$$?

Accepted Answer

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

Question 3

If a 200 g mass attached to a spring oscillates at a frequency of 2 Hz, what is its period $$T$$?

Accepted Answer

$$T = 0.5\ 	ext{s}$$

Question 4

Which equation represents the restoring force acting on a mass $$m$$ attached to a spring displaced by $$x$$ from equilibrium?

Accepted Answer

$$F_s = -kx$$

Question 5

Given the equation $$x(t) = A \cos(\omega t + \$$phi_0$$)$$, what does $$A$$ represent?

Accepted Answer

The amplitude of oscillation

Question 6

A mass-spring system has a spring constant $$k = 50\ 	ext{N/m}$$ and a mass $$m = 2\ 	ext{kg}. $$What is the angular frequency $$\omega$$?

Accepted Answer

$$\omega = 5\ 	ext{rad/s}$$

Question 7

Which of the following is true about the total energy $$E in a $$simple harmonic oscillator?

Accepted Answer

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

Question 8

At what position is the kinetic energy $$K of a $$mass-spring oscillator maximized?

Accepted Answer

At $$x = 0$$

Question 9

A 100 kg boat oscillates up and down 10 times in 20 s. When a dog sits in the boat, 10 oscillations take 22 s. What is the mass of the dog?

Accepted Answer

20 kg

Question 10

If the initial position $$x_i$$ and velocity $$v_i of a $$mass-spring oscillator are known, how can the amplitude $$A be $$determined?

Accepted Answer

$$A = \sqrt{x_i^2$ + \frac{v_i^2$}{\$$omega^2$$}}$$

Question 11

Which of the following best describes the relationship between frequency $$f$$ and angular frequency $$\omega$$?

Accepted Answer

$$f = \frac{\omega}{2\pi}$$

Question 12

In a simple harmonic oscillator, what is the maximum speed $$v_{max} of $$the mass?

Accepted Answer

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

Question 13

Which of the following is NOT an example of oscillatory motion in physics?

Accepted Answer

Linear motion of a car on a highway

Question 14

The equation $$m \frac{d^2$x}{dt^2$} = -kx$$ describes:

Accepted Answer

Simple harmonic motion

Question 15

If the phase constant $$\$$phi_0$$ is zero, what is the initial position x(0$$)$$ of a mass-spring oscillator?

Accepted Answer

$$x(0) = A$$

Question 16

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

Accepted Answer

Total energy remains constant

Question 17

A mass $$m$$ oscillates with amplitude $$A$$ and angular frequency $$\omega. $$What is the maximum acceleration $$a_{max}$$?

Accepted Answer

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

Question 18

Which of the following is a possible solution to the equation $$\frac{d^2$x}{dt^2$} = -\$$omega^2$$ x$$?

Accepted Answer

$$x(t) = A \cos(\omega t + \$$phi_0$$)$$

Question 19

If a mass-spring oscillator has initial velocity $$v_i$$ and initial position $$x_i$$, what is the expression for the phase constant $$\$$phi_0$$?

Accepted Answer

$$\$$phi_0$$ = -	an$$^{-1}$$\left(\frac{v_i}{\omega x_i}ight)$$

Question 20

Which of the following best describes the sum of two solutions to the equation $$\frac{d^2$x}{dt^2$} = -\$$omega^2$$ x$$?

Accepted Answer

The sum is a solution

Oscillatory Motion and Simple Harmonic Motion: Study Notes

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