Damped oscillations
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In the underdamped case, the transient solution of a second order differential equation consists of dying oscillations.
Plot the graph of
y=(e^(-0.5*t))*cos(10*pi*t+pi/4) for 0<=t<3, with a sampling interval of 0.01.
Considering two peaks, 2 seconds apart, calculate the proportional decrease in the oscillation between the peaks.
By analysing the exponential part of the function e^(-0.5*t), and two values t0 and t0+2, confirm this proportional decrease for any 2 second interval.
#differentialequations #dampedoscillations
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