Important SHM Graph Relations

Important SHM Graph Relations

### Displacement-Time Relation

$$x=A\sin(\omega t+\phi)$$

### Velocity-Time Relation

$$v=A\omega\cos(\omega t+\phi)$$

### Acceleration-Time Relation

$$a=-A\omega^2\sin(\omega t+\phi)$$

### Terminologies

- φ → Initial phase.

- ω → Angular frequency.

### Conditions / Special Cases

- Velocity leads displacement by:

$$\frac{\pi}{2}$$

- Acceleration is opposite to displacement:

$$a=-\omega^2x$$

### Usage

- Used in graph interpretation of SHM.