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 .

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**Video Explanation**

x-t, v-t and a-t Graphs of SHM

**Concept Test**

1401

1413

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