Question 152: Oscillations

Question

The amplitude of a damped oscillator decreases to $$0.9$$ times its original magnitude in $$5s$$. In another $$10s$$ it will decrease to $$\alpha $$  times its original magnitude, where $$\alpha $$ equals

Accepted Answer

as $$\,\,A = {A_0}{e^{{{bt} \over {2m}}}}$$ (where, $${A_0} = $$ maximum amplitude)
According to the questions, after $$5$$ second,
$$0.9{A_0} = {A_0}{e^{ - {{b\left( 5 ight)} \over {2m}}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i ight)$$
After $$10$$ more second,
$$A = {A_0}{e^{ - {{b\left( {15} ight)} \over {2m}}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} ight)$$
From eqns $$(i)$$ and $$(ii)$$
$$A = 0.729\,{A_0}$$
$$	herefore$$ $$\alpha  = 0.729$$

Answer

$$0.7$$

Answer

$$0.81$$

Answer

$$0.729$$

Answer

$$0.6$$

Oscillations

The amplitude of a damped oscillator decreases to $0.9 times its original magnitude in 5s. In another 10s it will decrease to \alpha times its original magnitude, where \alpha $ equals

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