# Damped oscillations

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 t

_{0}and t

_{0}+2, confirm this proportional decrease for any 2 second interval.

#differentialequations #dampedoscillations

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