The graph shows the mean power absorbed by an oscillator when driven by a force
ID: 1899413 • Letter: T
Question
The graph shows the mean power absorbed by an oscillator when driven by a force of constant magnitude but variable angular frequency W (omega). (a) At exact resonance, how much work per cycle is being done against the resistive force? Period = 2(pi)/W. (b) At exact resonance, what is the total mechanical energy E(naught) of the oscillator? (c) If the driving force is turned off, how many seconds does it take before the energy decreases to a value
E = E(naught)e^(-1) ?
The graph shows the mean power absorbed by an oscillator when driven by a force of constant magnitude but variable angular frequency W (omega). (a) At exact resonance, how much work per cycle is being done against the resistive force? Period = 2(pi)/W. (b) At exact resonance, what is the total mechanical energy E(naught) of the oscillator? (c) If the driving force is turned off, how many seconds does it take before the energy decreases to a value E = E(naught)e^(-1) ?Explanation / Answer
A)
Pmax =10 W
T=2/10^6
at resonance
work per cycle =Pmax*T
=10*2/10^6 =2*10^5 J
B)
Q=2*energy stored /energy lost per cycle
energy stored E0=(Q/2)*work done per cycle
Q =10^6/(1.005-0.995)*10^6=100
E0=100*10^-5 =10^-3 J
C)
energy decay time constant =m/b
m/b =Q/=100/10^6= 10^-4 sec
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