Amplitude in damped SHM:

$\overline{){\mathit{A}}{\mathbf{\left(}}{\mathbf{t}}{\mathbf{\right)}}{\mathbf{=}}{{\mathbf{A}}}_{{\mathbf{0}}}{{\mathbf{e}}}^{\raisebox{1ex}{$\mathbf{-}\mathbf{b}\mathbf{t}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{2}\mathbf{m}$}\right.}}$

Periodic time:

$\overline{){\mathbf{T}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{f}}}$

We'll determine the value of damping constant b using the conditions:

m = 0.2 kg

t = 50s

A(50s) = (60/100)A_{0} = 0.6A_{0}

A 200g oscillator in a vacuum chamber has a frequency of 2hz. When air is admitted, the oscillation decreases to 60% of its initial amplitude in 50s. How many oscillations will have been completed when the amplitude is 30% of its initial value?

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