Consider a system with a damping force undergoing forced oscillations at an angu
ID: 1962639 • Letter: C
Question
Consider a system with a damping force undergoing forced oscillations at an angular frequency omega: What is the ratio of the average kinetic energy to the average potential energy? Express the answer in the terms of the ratio For what value(s) of omega are the average kinetic energy and the average potential energy equal? What is the total energy of the system under these conditions? How does the total energy of the system vary with time for an arbitrary value of omega? For what values of omega is the total energy constant in time?Explanation / Answer
The kinetic energy of the oscillator=1/2 m2(a2-x2)
The potenial energy of the oscillator=1/2 m2x2
The ratio of kinetic energy to potential energy=(1/2 m2(a2-x2))/(1/2 m2x2)
=(a2-x2)/x2
Let the kinetic energy and potential energy are equal.
1/2 m2(a2-x2)=1/2 m2x2
a2-x2=x2
2x2=a2
x2=a2/2
x=2a
a sin t=2a
sin t=2
t=/4
=/4t
The kinetic energy and potential energy are equal at =/4t
The total energy is costanat.
Total energy=1/2 m2a2
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