Week 12 + 13 A2 - SHM Flashcards
SHM
An object is in simple harmonic motion when…
The acceleration is proportional to the displacement and acts in the opposite direction to the displacement.
Free Oscillations
An object oscillates at its own natural frequency after an initial force initiates the oscillation and is then removed.
Forced Oscillation
A force continuously acts on an object and causes either resonance or damping.
Resonance
Resonance occurs when the driver frequency is equal to the natural frequency of the object (assuming damping is close to 0), causing the amplitude of the object to increase significantly.
Damping
The decreasing of amplitude of an oscillator by a damping force acting in the opposite direction to its velocity.
Heavy Damping
The object returns to the equilibrium position very slowly when displaced, without oscillation (eg classroom door)
Light Damping
The amplitude decreases slightly with each oscillation (eg pendulum)
Critical Damping
The object returns to the equilibrium position as soon as possible without oscillation (eg car suspension or car speedometer needle)
shm acceleration equation
-ω^2 x
shm displacement equation
x = x(initial) cos ωt
shm velocity equation
v = -x(initial) ω sin ωt
acceleration shm equation
a = - x(initial) ω^2 cos ωt
angular velocity equation (2 versions)
ω = 2 πf ω = 2 π/T
Pendulum Period Equation
T = 2 π √(l/g)
Spring Mass System Period
T = 2 π √(m/k)
