Question

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/4

Answer 1

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)/b                                                                                                                                                                             For energy to become half, e^-bt/m = 1/2

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