10 Oscillations

Question 1

Simple harmonic motion

Answer 1

Motion of a body whose acceleration is directly proportional to its displacement from the equilibrium position and is always directed towards the equilibrium position
a=-kx

Question 2

SHM equations wrt time

Answer 2

1. x=x(max) sin ω t
2. v=v(max) cos ω t
3. a=-a(max) sin ω t

Question 3

SHM equations wrt x

Answer 3

v=+/- ω√[x(max)^2 - x^2]
a = -ω^2 x

Question 4

Damped oscillations

Answer 4

Oscillations in which the amplitude diminishes with time as a result of dissipative forces that reduces the total energy of the system

Question 5

Light damping

Answer 5

Amplitude decreases exponentially with time over a number of oscillations
Period of oscillations is slightly longer (but remains constsnt)

Question 6

Heavy damping

Answer 6

System returns to equilibrium very slowly

Question 7

Critical damping

Answer 7

System returns to equilibrium in the shortest time without oscillating

Question 8

Resonance

Answer 8

When the frequency at which an object is made to oscillate is equal to its natural frequency of vibration