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Consider the damped SHM of a spring mass system. If the time taken for the amplitude to become half is ‘T’, what is the time taken for mechanical energy to become half?(a) T(b) T/2(c) 2T(d) T/4I have been asked this question in a national level competition.My question is from Oscillations topic in section Oscillations of Physics – Class 11

Answer»

The correct answer is (b) T/2

The explanation is: Amplitude = Ae^-bt/2m& ENERGY = 1/2kA^2e^-bt/m.For amplitude to BECOME HALF, e^-bt/2m = 1/2

Or bT/2m = LN(2)

Or T = 2m ln(2)/bFor energy to become half, e^-bt/m = 1/2

Or t = m ln(2)/b = T/2.



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