A simple pendulum $$50$$ cm long is suspended from the roof of a cart accelerating in the horizontal direction with constant acceleration $$3gm/s2$$. The period of small oscillations of the pendulum about its equilibrium position (in$$ $$seconds) $$g=$$π$$2m/s2$$ is $$___________$$.

Question

A simple pendulum $$50$$ cm long is suspended from the roof of a cart accelerating in the horizontal direction with constant acceleration $$3gm/s2$$. The period of small oscillations of the pendulum about its equilibrium position (in$$ $$seconds) $$g=$$π$$2m/s2$$ is $$___________$$.

Infinity Learn · Accepted Answer

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

$\begin{array}{l} T = 2 π \sqrt{\frac{L}{g_{eff}}} where g_{eff} = \sqrt{g^{2} + (\sqrt{3 g})^{2}} = 2 g \\ \Rightarrow T = 1 .0 s \end{array}$

Applications of SHM

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

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Applications of SHM

Remember concepts with our Masterclasses.

A simple pendulum 50 cm long is suspended from the roof of a cart accelerating in the horizontal direction with constant acceleration 3gm/s2. The period of small oscillations of the pendulum about its equilibrium position (in seconds) g=π2m/s2 is ___________.

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=2πLgeff where geff=g2+(3g)2=2g⇒ T=1.0s

Ready to Test Your Skills?

free study material

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