Plot envelope of damped vibration.

[duzO]

Homework Statement

I have a under-damped vibration equation (below) that plots displacement vs time graph. Thing is i need to plot an envelope of the graph and it has to take into account initial speed v0.

Homework Equations

1. Equation which plots displacement vs time.
x(t)=exp^(-zeta*Wn*t) * ((x0 * cos(Wd*t)) + ((v0 + zeta * Wn * x0) /Wd)*sin(Wd*t))

zeta-damping ratio
wn- natural frequency
x0- initial displacement
wd- damped vibration freq (=sqrt(1-zeta^2)*wn)
v0 - initial speed
t-time

The Attempt at a Solution

Well I guess exponential decay multiply by something like (a*sin(b)) to account for the angle and rise of the wave.

x(t)=x0 * (?) * exp^(-zeta*wn*t)

Stupid question, I know, but please... :)

How to incorporate initial speed v0 and x0 into envelope equation so that it would plot correctly?

 

[hotvette]

I think you need to fit an exponential to two successive peaks.

 

[duzO]

yea i actually solved it :) never mind