Damped Oscillation

x = A e^{- \frac{b t}{2 m}} cos (ω^{'} t)

Displacement of a damped harmonic oscillator (underdamped case).

Variables

Displacement

Position from equilibrium

Initial amplitude

Amplitude at t = 0

Damping coefficient

Damping constant

kg/s

Time

Time elapsed

Mass

Oscillating mass

ω'

Damped angular frequency

ω' = √(ω₀² - (b/2m)²)

rad/s

Solution to m(d²x/dt²) + b(dx/dt) + kx = 0. The damped frequency is ω' = √(k/m - (b/2m)²).

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