SHM Graph Relations

## Displacement-Time Graph

### Formula

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

### Conditions

Sinusoidal curve.

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## Velocity-Time Graph

### Formula

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

### Phase Relation

$$\Delta\phi=\frac{\pi}{2}$$

Velocity leads displacement by 90°.

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## Acceleration-Time Graph

### Formula

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

### Phase Relation

$$\Delta\phi=\pi$$

Acceleration is opposite to displacement.

### Usage

- Used in graph-based SHM questions.