In Lab11 you studied the behavior of a harmonically oscillating system (a glider

Question

In Lab11 you studied the behavior of a harmonically oscillating system (a glider stretched between two springs) with presence of a damping force (provided by magnets taped to the skirt of the glider). The resulting amplitude of the oscillations was not just a simple harmonic motion, but a harmonic motion with exponentially decreasing amplitude. For a typical decay constant of your system tau = 10.0 s, how long should you wait for the amplitude of the oscillations to become 20 percent of the original amplitude measured at time t=0?

Explanation / Answer

given

T = 10 s,

at time t, A = 20% of Ao

A = 0.2*Ao

Apply,

A = Ao*e^(-t/T)

0.2*Ao = Ao*e^(-t/T)

0.2 = e^(-t/T)

ln(0.2) = -t/T

t = -T*ln(0.2)

= -10*ln(0.2)

= 16.09 s <<<<<<<<<<<---------Answer

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