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Q. Choose the correct statements regarding the expression $x(t)=A e^{-b t / 2 m} \cos \left(\omega^{\prime} t+\phi\right)$. Here, $\omega^{\prime}=\sqrt{\frac{k}{m}-\frac{b^{2}}{4 m^{2}}}, \frac{b}{\sqrt{k m}}$ is much less than 1 .

Oscillations

Solution:

The given expression represents the displacement for a damped oscillator. In this amplitude for a damped oscillation varies as $A e^{-b t / 2 m}$. But this oscillation is approximately periodic, if the damping is small. So, for the given displacement variation w.r.t. time is shown in the graph below. image
From this, we can conclude that the amplitude of the damped oscillator decreases with time.