Modelling oscillations

Question 1

Time Period

Answer 1

Time taken to complete one full oscillation

Will be constant for an oscillator irrespective of amplitude

T = 2π

Question 2

Amplitude

Answer 2

Maximum displacement (x) of the oscillation

Question 3

Angular velocity

Answer 3

ω = radians per second

ωt = 2πft

Question 4

Displacement

Answer 4

x = distance perpendicular to the equilibrium
A = radius of oscillator

= Acos(2πft) = Acos(ωt)
when started at maximum displacement

= Asin(2πft) = Asin(ωt)
when started at x=0

Question 5

Simple Harmonic Motion

Answer 5

Criteria:

• oscillator always pulled back to the equilibrium by a restoring force
• a is directly proportional to displacement
• a is always directed towards the equilibrium
• T is approximately isochronos

Question 6

SHM general formula

Answer 6

a = -kx
= -ω^2
= -4π^2f^2x (as ω = 2πf)

Question 7

s / v / a as relative graphs

Answer 7

s to v to a to s
sin cos -sin -cos

a = dv/dt = d^2x/dt^2

x = integral of v = integral of the integral of a

Question 8

Force and oscillators

Answer 8

a = F/m = -kx/m = d^2x/dt^2