Degrees of damping LO (i)
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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.
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