Question

Hi, how do I plot the function of simple harmonic motion with damping. I've only been given the general solution, no variables.

Answer 1

The fuction is:
mx ̈+cx ̇+kx=0

Answer 2

The general solution is:
x=Ae^(-βt) cos(ωt+ϕ)

Answer 3

start with a cosine wave amplitude A, so it goes +A to -A in the y axis. shift it along the x axis by phi. that's the first bit.

then it should decay exponentially, which is where the damping comes in. how quickly that happens depends on the nature of the damping.

here's a nice graphic
http://hyperphysics.phy-astr.gsu.edu/hbase/oscda2.html

Answer 4

I get the cosine wave part but how should i decide how much damping to plot from the information i have?

Answer 5

you have an infinite number of ways to do this.

you could go for critical damping or maybe do under, over a crit on the same chart

like the link i posted

sorry to be vague but your assignment sounds pretty vague too, from what is written above :p

Answer 6

yeah it is pretty vague, I think i'll go for under damping. Thanks for your help.