How Does Damping Affect the Energy of an Oscillator?

[Paddyod1509]

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

 

[Paddyod1509]

I have also assumed that y and x are interchangeable variables here, as no other information has been provided

 

[Mute]

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 $dE/dt$.

 

[pasmith]

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 E = C - mvx 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.