Question

0.25 0.2 0.15 0.1 a[m/s] -0.1 -0.15 EEEE -0.2 -0.25 0 10 20 30 50 60 70 80 40 t[s] Problem 2 One day, a large drilling platform (M= 9 x 10 kg) is floating in the ocean minding its own business when a tsunami passes by. The upward vertical acceleration vs time for the platform after the tsunami passes is measured by an accelerometer and plotted in the graph above. a) What is the damping constant b for this oscillation? b) What was the initial vertical displacement of the platform (give a positive answer if it was upwards and a negative answer if it was downwards)?

Answer 1

Write the expression for the damped harmonic oscillator. dr2 Here, 2 r = and as = m x = ae" sin ( ot +) (o= Vos? -2) a(t)= ae="I The decrement over a time period T as follows. ao = ei (a) From the given figure, a, = 0.2, = 0.125, and T =13 sec

1.1 0.2 13 (0.125 = 0.036154125 b=2rm = 2(0.036154125)(9x10') = 6.50774256 x 10 kg/s? (b) t=0 f(x a)=-0.225 m/sh2 **=-0.225 = -0.225 -0.225t + c =-0.225t+c 0.225t -- — = +ct+d 0.22512 - = - - +(0)t + 0 0.22512 =-0.112512 Hence, the first or initial displacement was downward, which is negative.