Question

58 For the damped oscillator system shown in Fig. 15-16, with m 250 g, k 85 N/m, and b - 70 g/s, what is the ratio of the oscil- lation amplitude at the end of 20 cycles to the initial oscillation amplitude?

Answer 1

Period

$T=2\pi \sqrt{\frac{m}{K}}=2\pi \sqrt{\frac{0.25}{85}}=0.3408 s$

From

$A=A_{o}e^{-bt/2m}$

$=>\frac{A}{A_{o}}=e^{-bt/2m}$

Given t=20T =20*0.3408

t=6.815 s

$=>\frac{A}{A_{o}}=e^{-0.07\times 6.815 /2\times 0.25}=0.385$