Part (a): The number of periods completed between time to = 0 ms and t1 = 0.9 ms are 10. Therefore the time period is,
Thus the angular frequency is,
Peak voltage at to is 70 V and at t1 is 40 V. The voltage in a damped oscillating circuit can be written as,
Here for peak value cos() =1. So the time constant is,
Now the resonant frequency is,
Now the capacitance can be calculated as,
Initial energy in the capacitor can be given as,
Now the energy after 17 periods can be calculated as,
Part (b): When 87% of initial energy is dissipated, that is,
Then the time is,
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