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.

NOTES:

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.