The period of oscillation of a simple pendulu | vedclass

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Question

(A) The vehicle moves down a frictionless inclined plane with an acceleration $a = g\sin \alpha$. In the frame of the vehicle,a pseudo force $F_p = ma

Vedclass · Accepted Answer

$2\pi \sqrt {\frac{L}{{g\cos \alpha }}} $

Vedclass · Answer

(A) The vehicle moves down a frictionless inclined plane with an acceleration $a = g\sin \alpha$. In the frame of the vehicle,a pseudo force $F_p = ma = mg\sin \alpha$ acts on the bob of the pendulum in the upward direction along the incline. The effective acceleration $g_{eff}$ is the vector sum of the acceleration due to gravity $\vec{g}$ and the negative of the vehicle's acceleration $-\vec{a}$. Resolving the components,the component of $g$ perpendicular to the incline is $g\cos \alpha$ and the component of $g$ parallel to the incline is $g\sin \alpha$. The pseudo force cancels the component $g\sin \alpha$. Thus,the effective acceleration is $g_{eff} = g\cos \alpha$. The time period of the simple pendulum is given by $T = 2\pi \sqrt{\frac{L}{g_{eff}}} = 2\pi \sqrt{\frac{L}{g\cos \alpha}}$.

The period of oscillation of a simple pendulum of length $L$ suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination $\alpha$,is given by

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