First slide

Simple hormonic motion

Question

A simple pendulum 50 cm long is suspended from the roof of a cart accelerating in the horizontal direction with constant acceleration $\sqrt{3}$ g $m / s^{2}$ . The period of small oscillations of the pendulum about its equilibrium position is ( $g = π^{2} m / s^{2}$ ):

Moderate

A

1.0 sec
B

1.25 sec
C

1.53 sec
D

1.68 sec

Solution

With respect to the cart, equilibrium position of the pendulum is shown.
If displaced by small angle $θ$ from this position, then it will execute SHM about this equilibrium position, time period of which is given by:
$T = 2 π \sqrt{\frac{L}{g_{eff}}}; g_{eff} = \sqrt{g^{2} + {(\sqrt{3} g)}^{2}}$
$\Rightarrow g_{eff} = 2 g \Rightarrow T = 1.0 second$

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