Fermion Labs

Parameters

Mass (m)2.0 kg

Spring Constant (k)10.0 N/m

Damping (b)0.50 Ns/m

Initial Displacement5.0 m

Position (x)

5.00 m

Velocity (v)

0.00 m/s

Total Energy

0.00 J

Live Equation

\ddot{x} = -\frac{b}{m}\dot{x} - \frac{k}{m}x

a = -\left(\frac{0.50}{2.00}\right)(+0.00) - \left(\frac{10.00}{2.00}\right)(+5.00)

Awaiting Telemetry

Governing Dynamics

A damped harmonic oscillator is governed by Newton's second law, where the restoring force of the spring and a damping force (like air resistance or internal friction) act on the mass.

m\frac{d^2x}{dt^2} + b\frac{dx}{dt} + kx = 0

Depending on the damping ratio $\zeta = \frac{b}{2\sqrt{mk}}$ , the system can be underdamped ( $\zeta < 1$ ), critically damped ( $\zeta = 1$ ), or overdamped ( $\zeta > 1$ ).