Oscillation

Question 1

Define Simple Harmonic Motion

Answer 1

2 conditions:
The acceleration is directly proportional to the displacement from the equilibrium position.
The acceleration is always directed towards the equilibrium position Or the direction of acceleration is always opposite to the displacement.
( a = -ω²x )

Question 2

How to prove simple harmonic motion

Answer 2

show that a (acceleration) proportional to -x (displacement)

angular frequency ω is constant. where ω is the rate of change of phase of particle.

Question 2

Equations of S.H.M

Answer 2

max a = ω²x0
v = -+ω√( x0² - x²)
v0 = ωx0

x = x0 sin( ωt ) #if t=0=equilibrium
x = x0 cos( ωt) #if t=0= amplitude
x0 is max displacement
x is displacement from equilibrium
max speed = equilibrium position, x = 0

Question 3

Define free oscillation

Answer 3

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

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

Question 3

Define forced oscillation

Answer 3

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

Question 3

Define damped oscillation

Answer 3

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

Question 4

Define resonance

Answer 4

Resonance is a phenomenon in which there is a maximum transfer of energy from the driver to the oscillating system in a forced oscillation.

The oscillating system achieves maximum amplitude during resonance.

For an undamped system, resonance occurs when the driving frequency equals to the natural frequency of the oscillating system.