Consider an underdamped motion of a body of mass m 15 kg If

Consider an underdamped motion of a body of mass m = 1.5 kg. If the time between two consecutive maxima is 3 sec and the maximum amplitude decreases to 1/2 its initial value after 15 cycles, what is the damping constant of the system?

Solution

Answer :

We are given by

T = 3sec

A = A_o exp ( - t)

1/2 = exp ( - * 3)

Apply logarithm on both sides, we get

ln ( 1/2 ) = - 3

0.69314718 = - 3

= 0.23104906