Remember that and ?
If we begin with
and differentiate both sides with respect to time, we obtain
and differentiate both sides with respect to time, again we obtain
With just two steps of differentiation, we learn that
- In a SHM, displacement, velocity and acceleration all vary sinusoidally with time.
- Acceleration leads velocity by a quarter cycle, and velocity in turn leads displacement by a quarter cycle.
- Maximum velocity
- Maximum acceleration .
x-t, v-t and a-t Graphs of SHM