Damped Oscillation

Damped Oscillation

### Definition / Formula

$$A=A_0e^{-\frac{bt}{2m}}$$

### Terminologies

- A → Amplitude after time t.

- A₀ → Initial amplitude.

- b → Damping constant.

- m → Mass of oscillating body.

- t → Time.

### Conditions / Special Cases

- Amplitude decreases exponentially with time.

$$A\rightarrow0\ (t\rightarrow\infty)$$

- Energy decreases as:

$$E\propto A^2$$

### Usage

- Used in real-life vibrating systems where energy loss occurs.