Question 1

A spring with a spring constant $$k is $$stretched by a distance $$x$$ from its equilibrium position. What is the magnitude of the restoring force exerted by the spring?

Accepted Answer

$$F = -kx$$

Question 2

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

Accepted Answer

Motion with a restoring force proportional to displacement and directed toward equilibrium

Question 3

A mass $$m$$ attached to a spring oscillates with angular frequency $$\omega. $$Which equation correctly relates $$\omega$$, $$k$$, and $$m$$?

Accepted Answer

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

Question 4

If the amplitude of a spring-mass system is doubled, what happens to the maximum velocity $$v_{max}$$?

Accepted Answer

It is doubled

Question 5

The displacement $$x of a $$mass in SHM is given by $$x = A \cos(\omega t). $$What is the expression for the velocity $$v_x$$?

Accepted Answer

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

Question 6

A spring is compressed from $$x_0 to$$ $$x_f. $$What is the work done by the spring during this process?

Accepted Answer

$$W = \frac{1}{2}k(x_0$^2 - x_f^2$)$$

Question 7

Which of the following is the correct expression for the elastic potential energy stored in a spring stretched by $$x$$?

Accepted Answer

$$PE_{elastic} = \frac{1}{2}kx^2$

Question 8

A spring-mass system oscillates with a period $$T. $$What is the frequency $$f of $$the oscillation?

Accepted Answer

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

Question 9

The total mechanical energy $$E of a $$spring-mass system in SHM is given by:

Accepted Answer

$$E = \frac{1}{2}mv^2$ + \frac{1}{2}kx^2$

Question 10

A mass $$m$$ attached to a spring with spring constant $$k is $$oscillating. If the mass is increased, what happens to the period $$T of $$oscillation?

Accepted Answer

The period increases

Question 11

Which of the following best explains why a spring-mass system continues to oscillate in the absence of friction?

Accepted Answer

There is no energy loss, so mechanical energy is conserved

Question 12

The maximum acceleration $$a_{max} of a $$mass in SHM is:

Accepted Answer

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

Question 13

A spring is stretched so that its displacement is $$x. If $$the spring constant is $$k$$, what is the average force exerted by the spring during the stretch from $$x_0 to$$ $$x_f$$?

Accepted Answer

$$F_{avg} = \frac{k(x_0$ - x_f)}{2}$$

Question 14

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

Accepted Answer

The velocity is always constant

Question 15

If a spring is compressed and then released, which of the following best describes the energy transformation?

Accepted Answer

Elastic potential energy is converted to kinetic energy

Question 16

A spring-mass system is oscillating with amplitude $$A. At $$what position is the kinetic energy maximum?

Accepted Answer

At $$x = 0$$

Question 17

The angular frequency $$\omega of a $$spring-mass system is related to the frequency $$f by$$:

Accepted Answer

$$\omega = 2\pi f$$

Question 18

A spring-mass system is set into motion and a pen traces its displacement over time. What type of graph is produced?

Accepted Answer

A sinusoidal graph

Question 19

Which of the following equations correctly represents the total mechanical energy for a system involving both translational and rotational motion, gravity, and a spring?

Accepted Answer

$$E = \frac{1}{2}mv^2$ + \frac{1}{2}I\$$omega^2$$ + mg h + \frac{1}{2}kx^2$

Simple Harmonic Motion: Springs, Kinematics, and Energy- lecture 23

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