Combination of Two SHMs (Same Frequency)

Combination of Two SHMs (Same Frequency)

### Formula

$$x=x_1+x_2$$

### Resultant Amplitude

$$A=\sqrt{A_1^2+A_2^2+2A_1A_2\cos\phi}$$

### Terminologies

- A → Resultant amplitude of combined SHM.

- A₁, A₂ → Amplitudes of individual oscillations.

- φ → Phase difference between two oscillations.

### Conditions / Special Cases

- Same phase:

$$\phi=0$$

$$A=A_1+A_2$$

- Opposite phase:

$$\phi=\pi$$

$$A=|A_1-A_2|$$

### Usage

- Used in superposition of oscillations with same frequency.