Damped Oscillator Equation

  • #1
the damped oscillator equation:

(m)y''(t) + (v)y'(t) +(k)y(t)=0

Show that the energy of the system given by

E=(1/2)mx'² + (1/2)kx²

satisfies:

dE/dt = -mvx'


i have gone through this several time simply differentiating the expression for E wrt and i end up with

dE/dt = x'(-vx')

im at a brick wall. Am i doing something wrong? Any help is much appreciated! Thanks
 

Answers and Replies

  • #2
I have also assumed that y and x are interchangeable variables here, as no other information has been provided
 
  • #3
Mute
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I don't see anything wrong with your calculation. In fact, double check the units for your expressions - I don't think the suggested answer "##m\gamma \dot{x}##" even has the same units as ##dE/dt##.
 
  • #4
pasmith
Homework Helper
1,910
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the damped oscillator equation:

(m)y''(t) + (v)y'(t) +(k)y(t)=0

Show that the energy of the system given by

E=(1/2)mx'² + (1/2)kx²

satisfies:

dE/dt = -mvx'
That must be wrong: it requires that [itex]E = C - mvx[/itex] for some constant C, which is not the case.

i have gone through this several time simply differentiating the expression for E wrt and i end up with

dE/dt = x'(-vx')
That is the right expression for dE/dt.
 

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