In any real system that friction is not negligible; the amplitude of an oscillat

Question

In any real system that friction is not negligible; the amplitude of an oscillation will eventually diminish without driven force. This is called underdamped oscillation. The resulting oscillation will look something like this The equation for this graph is x(t) = Ae^-t/2 tau cos(omega_d + phi) where omega_d is the damping angular frequency and tau is the time constant for the damping = b/m where b is the damping coefficient. This happens when an oscillator is moving through a viscous medium at low speed v so the damping force is F_d = -bv. One way of describing this mathematically is to say that an "exponential envelope" is bounding the sinusoidal curve. So we could say that the maximum amplitude of the oscillator is given by x_max (t) = A e^-t/2t A is the initial amplitude of the oscillator at t = 0, x_max(t) is the amplitude of the oscillator at instant t. Tape a paper plate to the bottom of the mass as shown in the picture. Displace the mass from equilibrium and start recording the position again in Logger Pro. This time the mass will come to rest fairly soon. What type of damping does the system undergo, under damping, over damping or critical damping? Support your answer with explanation.

Explanation / Answer

For critical and overdamped case the particle takes infinite time to come back to the origin, or in other words it doesn't cross the origin. Here the damping is not that high, and the mass crosses the origin indeed. So, it's an example or underdamped motion with small tau.

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