A body executes SHM when its acceleration is directly proportional to its displacement but in the opposite direction.
Simple harmonic motion is an idealised time of oscillating motion.
Quantity Symbol Definition Units:
- Amplitude (A): the maximum displacement from the equilibrium position. Units = m
- Period (T): the time for one complete oscillation. Units = s
- Frequency (f): the number of oscillations in 1 second. Note that f = 1/T Hz
- Displacement (s): how far the object is from its equilibrium (rest) position. Units= m
The vertical displacement of a mass on a spring varies sinusoidally with time:
s = Asinwt (A=Amplitude, w= 2 x pi x f)
The velocity of a mass on a spring also varies this way,however when displacement is greatest, the velocity is zero, therefore the velocity forms a cosine graph.
v = wAcoswt When velocity is max, v=wA
Acceleration is the change in velocity over time (dv/dt), so to get the acceleration we must differentiate the equation for velocity to get:
a = -w^2Asinwt (therefore a=-w^2s)
- the resultant force will be proportional to the displacement ( as …