Q: If the restoring force of a spring is 6 N when the displacement is 0.03 m, what is the potential energy stored in the spring at this displacement?

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} \times 200 \times (0.03)^2$ = 0.09\ \mathrm{J}$$

Question 1

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

Accepted Answer

A back-and-forth motion where the restoring force is proportional to the displacement from equilibrium.

Question 2

A spring obeys Hooke's law. If a 0.5 kg mass attached to the spring causes a restoring force of 6 N when displaced by 0.03 m, what is the spring constant $$k$$?

Accepted Answer

$$k = \frac{6}{0.03} = 200\ \mathrm{N/m}$$

Question 3

Which of the following is the correct expression for the position $$x(t) of an $$object in SHM starting from its maximum displacement?

Accepted Answer

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

Question 4

What is the relationship between the frequency $$f$$ and the period $$T of an $$oscillating system?

Accepted Answer

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

Question 5

For a mass-spring system in SHM, which of the following correctly gives the angular frequency $$\omega$$?

Accepted Answer

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

Question 6

At what position is the velocity of an object in SHM maximum?

Accepted Answer

At the equilibrium position ($$x = 0)$$

Question 7

Which of the following statements about energy in SHM is correct?

Accepted Answer

Total mechanical energy is conserved and is the sum of kinetic and potential energy.

Question 8

If the amplitude of a spring-mass system is doubled, how does the total mechanical energy change?

Accepted Answer

It increases by a factor of 4.

Question 9

A 0.5 kg mass oscillates on a spring with $$k = 200\ \mathrm{N/m}. $$What is the period $$T of $$oscillation?

Accepted Answer

$$T = 2\pi \sqrt{\frac{0.5}{200}} \approx 0.314\ \mathrm{s}$$

Question 10

Which of the following factors does NOT affect the frequency of a mass-spring system in SHM?

Accepted Answer

The amplitude of oscillation

Question 11

The restoring force in SHM is given by Hooke's law. Which equation correctly represents this force?

Accepted Answer

$$F = -kx$$

Question 12

In the context of SHM, what is the physical meaning of the equilibrium position?

Accepted Answer

It is the position where the net force on the object is zero.

Question 13

Which of the following correctly describes the relationship between SHM and uniform circular motion?

Accepted Answer

The projection of uniform circular motion onto one axis produces SHM.

Question 14

What is the maximum acceleration $$a_{max} of a $$mass in SHM with amplitude $$A$$ and angular frequency $$\omega$$?

Accepted Answer

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

Question 15

A glider oscillates with amplitude $$A. $$Where is its velocity zero?

Accepted Answer

At the maximum displacement ($$x = \pm A)$$

Question 16

If the restoring force of a spring is 6 N when the displacement is 0.03 m, what is the potential energy stored in the spring at this displacement?

Accepted Answer

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 200 	imes (0.03)^2$ = 0.09\ \mathrm{J}$$

Question 17

Which of the following is true about the direction of acceleration in SHM?

Accepted Answer

It is always directed toward the equilibrium position.

Question 18

A mass-spring system oscillates with amplitude $$A$$ and angular frequency $$\omega. $$What is the velocity $$v at $$displacement $$x$$?

Accepted Answer

$$v = \omega \sqrt{A^2$ - x^2$}$$

Question 19

If a mass attached to a spring is increased, what happens to the frequency of oscillation?

Accepted Answer

The frequency decreases.

Chapter 11: Periodic Motion – Simple Harmonic Motion (SHM) Study Notes

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