Further mechanics

Question 1

What is the definition of displacement in simple harmonic motion (SHM)?

Answer 1

Displacement is a vector quantity that signifies the distance from the oscillator to the equilibrium position.

Question 2

What is amplitude in SHM?

Answer 2

Amplitude (A) is the maximum displacement from the equilibrium position.

Question 3

Define the time period 𝑇 in oscillations

Answer 3

The time period T is the time taken to complete one full oscillation.

Question 4

What is the frequency 𝑓 in SHM?

Answer 4

Frequency f is the number of oscillations per unit time.

Question 5

What is angular frequency ω in SHM?

Answer 5

Angular frequency 𝜔ω is the rate of change of angular displacement, given by 𝜔=2𝜋𝑓ω=2πf or 𝜔=2𝜋𝑇ω= T2π
​
.

Question 6

What are the two defining characteristics of SHM?

Answer 6

(1) The acceleration is directly proportional to displacement.
(2) The acceleration is always directed towards the equilibrium position.

Question 7

What is the defining equation for SHM?

Answer 7

The acceleration 𝑎 is proportional to the displacement
𝑥

Question 8

How can you measure the frequency of a simple harmonic oscillator using an experiment?

Answer 8

Displace the mass, use a fiducial marker at the equilibrium position, measure 10 time periods, then divide by 10 to find
𝑇
T. Calculate frequency using 𝑓=1𝑇f= T1
​
.

Question 9

When do you use 𝑥=Acos(𝜔𝑡)x=Acos(ωt) and 𝑥=𝐴sin⁡(𝜔𝑡)
x=Asin(ωt) in SHM?

Answer 9

Use 𝑥=𝐴cos(𝜔𝑡)x=Acos(ωt) when the oscillator is at maximum displacement (amplitude) at 𝑡=0t=0. Use 𝑥=𝐴sin(𝜔t)x=Asin(ωt) when the oscillator starts at equilibrium at 𝑡=0
t=0.

Question 10

How does damping affect the amplitude and time period of an oscillating system?

Answer 10

Damping decreases the amplitude but does not change the time period.

Question 11

What happens to the amplitude and time period with heavy damping?

Answer 11

With heavy damping, the amplitude decreases more rapidly, but the time period remains unaffected.

Question 12

What is free oscillation?

Answer 12

Free oscillation occurs when the system is disturbed initially and then oscillates with no external forces, oscillating at its natural frequency.

Question 13

What is forced oscillation?

Answer 13

Forced oscillation occurs when an external driving force is applied during the oscillation.

Question 14

What is resonance?

Answer 14

Resonance occurs when the driving frequency matches the natural frequency of the system, causing a dramatic increase in amplitude.

Question 15

What happens to the amplitude when the driving frequency equals the natural frequency in resonance?

Answer 15

The amplitude increases dramatically.

Question 16

What effect does damping have on the resonance peak?

Answer 16

Damping lowers the amplitude at all points and shifts the peak amplitude to a lower frequency.

Question 17

Describe the resonance curve with and without damping.

Answer 17

Without damping, the resonance curve has a sharp peak at the natural frequency. With damping, the amplitude is lower at all frequencies, and the peak occurs at a lower frequency.

Question 18

Give two examples of resonance.

Answer 18

(1) Microwave oven: EM radiation frequency matches the natural frequency of water molecules, increasing their kinetic energy.
(2) Oscillating bridge: Driving force from wind or people matches the natural frequency of the bridge, causing large vibrations.

Question 19

What is damping in simple harmonic motion (SHM)?

Answer 19

Damping is the process by which energy is lost from an oscillating system, usually due to resistive forces such as friction or air resistance. This causes a gradual reduction in the amplitude of the oscillation over time. There are three types of damping:

Question 20

What is resonance in oscillations?

Answer 20

Resonance occurs when the frequency of a driving force matches the natural frequency of an oscillating system. This causes a significant increase in the amplitude of the oscillations. Examples include the resonance of water molecules in a microwave oven and the dangerous oscillations of a bridge due to wind or people walking.

Question 21

Three types of damping

Answer 21

Light damping: Amplitude decreases gradually without affecting the time period.
Heavy damping: Amplitude decreases significantly, and the system returns to equilibrium slowly without oscillating.
Critical damping: The system returns to equilibrium in the shortest possible time without oscillating.

Question 22

Name a feature of resonance

Answer 22

At resonance, energy is transferred most efficiently into the system, resulting in the maximum amplitude.