Damped Simple Harmonic Motion

Underdamped Overdamped Critically Damped

U-choose the damping and initial v:

b=   Note: keep b positive

v0=   Note: keep |v|<12

Check this box to see velocity, too

Once the box is selected/deselected you must reinitialize your choice.


The critically damped oscillator approaches equilibrium the fastest.

For the critically damped and overdamped cases, different initial conditions can lead to three possible scenarios for the motion:

a. b = 3, v0 = 0: object approaches equilibrium monotonically.

b. b = 2, v0 = 10: object attains a single extremum before approaching equilibrium.

c. b = 3, v0 = -10: object passes through equilibrium position, attains an extremum, then approaches equilibrium asymptotically.

Reference: Jerry B. Marion and Stephen T. Thornton, Classical Dynamics of Particles and Systems (4th edition, 1995) p. 116-125.

* This demonstration was written by Tim Gfroerer and scripted by Mario Belloni.