In the figure below, a damped simple harmonic oscillator has mass m = 260 g, k =
ID: 1908780 • Letter: I
Question
In the figure below, a damped simple harmonic oscillator has massm=260g,k=100N/m, andb=75g/s. Assume all other components have negligible mass. What is the ratio of the amplitude of the damped oscillations to the initial amplitude at the end of 20 cycles (Adamped/Ainitial)?
Explanation / Answer
In the figure below, a damped simple harmonic oscillator has massm = 230 g, k =70 N/m, and b = 60 g/s. Assume all other components havenegligible mass. What is the ratio of the amplitude of the dampedoscillations to the initial amplitude at the end of 20 cycles(Adamped / Ainitial)?
given
mass m = 0.23 kg
b =0.06 kg/s
time perod T =2*m/k
= 2*0.23/70
= 0.360s
the amplitude at t = 0 is given as
A = xm*e-b(0)/2m
A =xm ------(1)
the amplitude A1 at time t1 is given as
A1 = xm*e-bt1/2m
where t1 = 20T
= 20*0.360s
= 7.2s
so A1 =xme-b7.2/2m -----(2)
from (1) & (2) we have
A1/A = e-b7.2/2m
= e-0.06*7.2/2*0.23
= 0.390
Hope this may help you.