Question 1

Which of the following best describes the definition of Simple Harmonic Motion (SHM)?

Accepted Answer

A motion where the restoring force is proportional to the displacement and acts in the opposite direction to the displacement.

Question 2

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

Accepted Answer

The angular frequency of the motion.

Question 3

Which of the following is the correct expression for the velocity in SHM?

Accepted Answer

$$v(t) = -A \omega \sin(\omega t + \phi)$$

Question 4

If the acceleration in SHM is given by $$a(t) = -\$$omega^2$$ x(t)$$, what is the physical meaning of the negative sign?

Accepted Answer

It indicates that acceleration is directed opposite to the displacement.

Question 5

A mass-spring system oscillates with a period $$T. $$Which equation correctly relates the period to the mass $$m$$ and spring constant $$k$$?

Accepted Answer

$$T = 2\pi \sqrt{\frac{m}{k}}$$

Question 6

Which of the following is the correct formula for the total mechanical energy in SHM?

Accepted Answer

$$E = \frac{1}{2} m \$$omega^2$$ A^2$

Question 7

If a block attached to a spring is displaced and released, which of the following statements is true at the equilibrium position?

Accepted Answer

The kinetic energy is maximum.

Question 8

A pendulum exhibits SHM for small angles. Which of the following is the correct expression for its period $$T$$?

Accepted Answer

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

Question 9

Which of the following best describes the phase constant $$\phi in $$the SHM equation $$x(t) = A \cos(\omega t + \phi)$$?

Accepted Answer

It determines the initial position of the oscillator.

Question 10

A mass $$m$$ attached to a spring with constant $$k is $$set into SHM. If the amplitude is doubled, what happens to the total mechanical energy?

Accepted Answer

It quadruples.

Question 11

Which of the following is the correct relationship between angular frequency $$\omega$$, spring constant $$k$$, and mass $$m$$ for a mass-spring system?

Accepted Answer

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

Question 12

At what point during SHM is the restoring force at its maximum value?

Accepted Answer

At the maximum displacement (amplitude).

Question 13

A block oscillates on a frictionless surface attached to a spring. If the mass is increased, what happens to the period of oscillation?

Accepted Answer

It increases.

Question 14

Which of the following is the correct expression for the potential energy stored in a spring at displacement $$x$$?

Accepted Answer

$$U = \frac{1}{2} k x^2$

Question 15

If the frequency of a mass-spring system is $$f$$, what is the correct formula for the angular frequency $$\omega$$?

Accepted Answer

$$\omega = 2\pi f$$

Units, Physical Quantities, and Vectors: Fundamental Concepts

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