# Damped SHM

**Classical Mechanics**Level 5

Consider a simple pendulum, oscillating in air with a spherical bob, whose amplitude decreases from 10 cm to 8 cm in 40 seconds.

Assuming Stoke's law to be valid, find the time in seconds (rounding off to the greatest integer less than or equal to it ) in which amplitude of this pendulum will reduce from 10 cm to 5 cm in carbon dioxide.

**Details and Assumptions**

\(\dfrac{\eta_{\text{air}}}{\eta_{\ce{CO_2}}} = 1.3\).

\(\eta\) represents coefficient of viscosity.

Use the approximations, \(\ln 5 = 1.609\) and \(\ln 2 = 0.693\).

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