Simple harmonic motion Flashcards
definition of simple harmonic motion
The motion of a particle about a fixed point such that its acceleration is proportional to its displacement from a fixed point and is directed towards the fixed point.
what is the Period (T)
the time taken to complete one full cycle and return to start position
what is the frequency
the number of complete oscillations
frequency equation
1/time
period equation (T)
1/frequency
what does simple harmonic motion link acceleration with
the displacement from centre of oscillation (X)
Displacement(X) Equation
Acosωt
velocity equation
-Aωsinωt
acceleration equation
-Aω^2cosωt
equation for Hooke’s law
Force(F) =constant(K) X extension(x)
Angular frequency equation
ω=2πf=2π/T
period T of simple pendulum length
⊤=2π√(l/g)
period T of simple pendulum mass
⊤=2π√(m/k)
acceleration equation
a = -ωx^2
what is damped Oscillations
damping is the conversion of kinetic energy into heat energy until all the kinetic energy is lost. this is caused by air and friction.
when does forced oscillation occur
forced oscillation is when a periodic driving force is applied to a body capable of vibrating.
what is resonance
when frequency of driving force equals the natural frequency of a system, large amounts of amplitude and vibration will occur.
what happens during heavy damping
the displacement reduces almost exponentially to zero
what happens during light damping
the amplitude of oscitation is reduced to almost exponentially to zero
what happens when a body undergoes free oscillation
it vibrates at its natural frequency
