Soilwork
May2-04, 02:56 AM
Hey can someone guide me in the right direction here.
Q. Show that the time rate of change of mechanical energy for a damped , ubdriven oscillator is given by dE/dt=-bv^2 and hence is always negative.
Proceed as follows: Differentiate the expression for the mechanical energy of an oscillator, E=1/2mv^2 + 1/2kx^2. And use this equation:
-kx-b(dx/dt)=m(d^2x/dt^2)
I know it tells you how to approach the question and all, but I guess the main problem is that my differentiation isn't that great.
Anyway for the Energy equation I was thinking that you could change the v to change in x over change in time. delta(x)/delta(t)
not sure though.
Any help would be appreciated.
Q. Show that the time rate of change of mechanical energy for a damped , ubdriven oscillator is given by dE/dt=-bv^2 and hence is always negative.
Proceed as follows: Differentiate the expression for the mechanical energy of an oscillator, E=1/2mv^2 + 1/2kx^2. And use this equation:
-kx-b(dx/dt)=m(d^2x/dt^2)
I know it tells you how to approach the question and all, but I guess the main problem is that my differentiation isn't that great.
Anyway for the Energy equation I was thinking that you could change the v to change in x over change in time. delta(x)/delta(t)
not sure though.
Any help would be appreciated.