Angular SHM and Simple Pendulum

Practice Questions:

Question 1: difficult

Two simple pendulums of length 1 m and 16m respectively are both given small displacement in the same direction at the same instant. They will be again in phase after the shorter pendulum has completed n oscillations. The value of n is :

1. 1/3

2. 2/3

3. 1

4. 4/3

View Answer

\[ T = 2\pi\sqrt{\frac{l}{g}} \]

\[ T_{1}= 2\pi\sqrt{\frac{1}{g}}= 2 sec \]

\[ T_{2}= 2\pi\sqrt{\frac{16}{g}}= 8 sec \]

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Question 2: difficult

A simple pendulum 50 cm long is suspended from the roof of a cart accelerating in the horizontal direction with constant acceleration √3g m / s² .The period of small oscillations of the pendulum about its equilibrium position is (g = π² m/s²):

1. 1.0 sec

2. 1.25 sec

3. 1.53 sec

4. 1.68 sec

View Answer

\[ T = 2\pi\sqrt{\frac{l}{\sqrt{a^{2}+g^{2}}}} \]

\[ T = 2\pi\sqrt{\frac{0.5}{\sqrt{\left( \sqrt{3}g \right)^{2}+g^{2}}}} \]

\[ T = 2\pi\sqrt{\frac{0.5}{2g}} \]

\[ T = 2\pi\frac{1}{2\sqrt{g}} = 2\pi\frac{1}{2\pi}= 1 sec \]

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