8. For the damped string equation $u_{tt} - c^2 u_{xx} + ru_t = 0$, $r > 0$, show that the energy decreases.
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In this case, the potential energy is given by the square of the displacement of the string, while the kinetic energy is given by the square of the velocity of the string. Show more…
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Transcript
For this problem on the topic of second order linear ODE's, we want to find the steady state oscillation of the system that is modeled by the given ODE, which is 4Y double prime plus 8Y prime plus 13Y equal to 8 sine 1 .5T. Now from this equation, we know…
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