Tuesday, January 13, 2015

SHM Chapter 20 damping x vs t

Degrees of damping                    LO (i)


http://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHM20/SHM20_Simulation.xhtml


If no frictional forces act on an oscillator (e.g.  mass-spring system, simple pendulum system,  etc.), then it will oscillate indefinitely.

In practice, the amplitude of the oscillations decreases to zero as a result of friction. This type of motion is called damped harmonic motion. Often the friction arises from air resistance (external damping) or internal forces (internal damping).

if the motion is x= x0 sin(ωt), the following are the x vs t graphs for 2 periods, as an illustration of the damping.



when b=0.0 no damping, system oscillates forever without coming to rest. Amplitude and thus total energy is constant



when b=0.1 very light damping, system undergoes several oscillations of decreasing amplitude before coming to rest. Amplitude of oscillation decays exponentially with time.



when b=2.0 critically damp, system returns to equilibrium in the minimum time, without overshooting or oscillating about the equilibrium position amplitude and thus total energy is constant.



when b=5.0 very heavy damp, system returns to equilibrium very slowly without any oscillation


a more typical starting position, is  x= x0 cos(ωt), the following are the x vs t graphs for 2 periods, as an illustration of the damping.








when b=0.0 no damping, system oscillates forever without coming to rest. Amplitude and thus total energy is constant



when b=0.1 very lightly damp, System undergoes several oscillations of decreasing amplitude before coming to rest. Amplitude of oscillation decays exponentially with time.



when b=2.0, Critically damp, system returns to equilibrium in the minimum time, without overshooting or oscillating about the equilibrium position amplitude.



when b=5.0, very heavy damp, system returns to equilibrium very slowly without any oscillation.


Model:

http://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHM20/SHM20_Simulation.xhtml