A simple pendulum of length l is suspended from the ceiling of a cart which is sliding without friction on an inclined plane of inclination θ . What will be the time period of the pendulum?

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TestHub · Accepted Answer

Here, the point of suspension has an acceleration. $\vec{a}$ $= g \sin θ$ (down the plane). Further, $\vec{g}$ can be resolved into two components g sin θ (along the plane) and g cos θ (perpendicular to the plane).

${\vec{g}}_{eff} = \vec{g} - \vec{a}$

$= g \cos θ$ (perpendicular to plane)

$T = 2 π \sqrt{\frac{l}{| {\vec{g}}_{eff} |}}$

$= 2 π \sqrt{\frac{l}{g cos θ}}$

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