


Damped SHM








Damping proportional to velocity

 Three cases:
 Lightly damped SHM:
There is an oscillation but the amplitude decreases exponentially with time.
 Heavily damped SHM:
There is no real oscillation. There is only a very slow return of the object to the initial equilibrium position.
 Critically damped SHM:
There is no real oscillation.
It returns to the equilibrium position in the shortest time.
 The period of a lightly damped SHM is slightly longer than that of the undamped.
 Test for exponential decay:
A_{o}/A_{1} = A_{1}/A_{2} = A_{2}/A_{3} = .....

Damping due to Solid Friction

 The amplitude decreases linearly with time. Therefore,
A_{o}  A_{1} = A_{1}  A_{2} = A_{2}  A_{3} = .....
 The oscillator may finally stop at a point with nonzero displacement.




