Plot envelope of damped vibration.

In summary, the problem discussed is about plotting an envelope of a displacement vs time graph for an under-damped vibration equation. The equation takes into account initial speed and displacement, and involves the damping ratio, natural frequency, and time. The attempt at a solution involves fitting an exponential to two successive peaks. The problem was eventually solved.
  • #1
duzO
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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?
 
Last edited:
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  • #2
I think you need to fit an exponential to two successive peaks.
 
Last edited:
  • #3
yea i actually solved it :) never mind
 

1. What is a plot envelope of damped vibration?

A plot envelope of damped vibration is a graphical representation of the amplitude and frequency of a damped vibration over time. It shows the maximum amplitude that the system will reach at each frequency.

2. How is a plot envelope of damped vibration calculated?

The plot envelope of damped vibration is calculated by taking the maximum amplitude of the damped vibration at each frequency and plotting it against the corresponding frequency.

3. What information can be obtained from a plot envelope of damped vibration?

A plot envelope of damped vibration provides information about the behavior and characteristics of a damped vibration, including the natural frequency, damping ratio, and amplitude at different frequencies.

4. How is a plot envelope of damped vibration useful in engineering?

In engineering, a plot envelope of damped vibration is useful for analyzing and designing structures and systems that are prone to vibrations, such as buildings, bridges, and vehicles. It can also be used to identify potential issues and make adjustments to improve the performance and durability of a structure.

5. How does damping affect the plot envelope of damped vibration?

Damping affects the plot envelope of damped vibration by reducing the amplitude of the vibration over time. As the damping ratio increases, the plot envelope becomes narrower and the amplitude decreases, indicating a more stable and less oscillatory system.

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