Oscillations

Question 1

What are the conditions for Simple Harmonic Motion?

Answer 1

1. The acceleration is directly proportional to the displacement from the equilibrium position.
   a = -ω^2x
2. The acceleration is always directed towards the equilibrium position OR the direction of acceleration is always opposite to the displacement.
   ω = 2π/T = 2πf

Question 2

Find variation of v with displacement x

Answer 2

v = ±√x0^2-x^2
v0 = ωx0

Question 3

What is free oscillation?

Answer 3

In a free oscillation, there is neither resistive forces nor driving forces acting on the system. Thus, total energy is always constant and it oscillates with constant amplitude.

In a free oscillation, the object oscillates with a frequency called its natural frequency, f0

Question 4

What is damped oscillation?

Answer 4

A damped oscillation is one which experiences resistive forces.
The oscillating system loses energy until it comes to a stop

Question 5

State and explain an example of light-damping.

Answer 5

Amplitude will decrease gradually over time, but the period T remains constant over time.
The period T is higher than an undamped system.
The greater the degree of damping, the more drastic the decrease in amplitude.
e.g. Object oscillating in vacuum vs air vs water vs oil.

Question 6

State and explain an example of critical damping.

Answer 6

Body does not oscilate but returns to its equilibrium position in the shortest possible time.
e.g. (car suspension system, needle of measuring instrument.

Question 7

State and explain an example of heaving damping/over-damping.

Answer 7

Body will take a long time to return to its equilibrium position without oscillating.
e.g. door with dampers allow door to swing close gently

Question 8

What is a forced oscillating system?

Answer 8

A forced oscillating system is one that is driven by an external periodic driving oscillator or driver. There is continuous energy input to the oscillating system by the driver, and the system oscillates at the frequency of the driver.

Question 9

What is resonance?

Answer 9

Resonance is the phenomenon in which there is a maximum transfer of energy from the driver to the osillating system in a forced oscillation.
The oscillating system achieves maximum amplitude during resonance.
For an undamped system, resonance occurs when the driving frequency equals the natural frequency of the oscillating system.

Question 10

Features of a resonance curve

Answer 10

Curve shifted lower with increased damping (amplitude is smaller at all frequencies)
Flatter peak at resonance with increased damping (resonance occur at wider range of frequencies)
Peak skewed to the left with increased damping (resonance occurs at lower frequency)