Show that the time rate of change of mechanical energy for a damped, undriven oscillator is given by = -bv² and hence is always negative. To do so, differentiate the expression for the of an oscillator, E = }mv² + kx², and use Equation 15.31. mechanical energy Equation 15.31: -kx – b = m d²r

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Show that the time rate of change of mechanical energy for a damped, undriven oscillator is
given by 4 = -bv² and hence is always negative. To do so, differentiate the expression for the
mechanical energy of an oscillator, E = ;mv² + kx², and use Equation 15.31.
dE
Equation 15.31: – kx –
b = m
d²x
dt2
Transcribed Image Text:Show that the time rate of change of mechanical energy for a damped, undriven oscillator is given by 4 = -bv² and hence is always negative. To do so, differentiate the expression for the mechanical energy of an oscillator, E = ;mv² + kx², and use Equation 15.31. dE Equation 15.31: – kx – b = m d²x dt2
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