Second-Order Linear ODE: Vibration

Mode

System Parameters

Mass $m$ 1.00

Damping $c$ 0.50

Stiffness $k$ 4.00

Underdamped: $\zeta < 1$

Forcing

Amplitude $F_0$ 1.00

Frequency $\omega$ 1.00

        $\omega_n = 2.00$  ($\omega/\omega_n = 0.50$)
      

Initial Conditions

$x(0)$

$\dot{x}(0)$

Animation

Speed 1.0×

Display

Time range 20

Show envelope Show phase portrait

Governing Equation

Spring–Mass–Damper Animation

spring

damper

t = 0.00

Displacement $x(t)$

$x(t)$

envelope

Phase Portrait $(x, \dot{x})$

Energy

KE

PE

Total

Analytical Solution