Damped oscillations
Home >
All Problems > 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 t0 and t0+2, confirm this proportional decrease for any 2 second interval.
#differentialequations #dampedoscillations
plotXpose app is available on Google Play and App Store
Google Play and the Google Play logo are trademarks of Google LLC.
A version will shortly be available for Windows.
A version will shortly be available for Windows.
plotXpose app is a companion to the book Mathematics for Electrical Engineering and Computing by Mary Attenborough, published by Newnes, 2003.