Question

The bob of a simple pendulum is released at time \( t = 0 \) from a position of small angular displacement. Its linear displacement is \( l \) (length of simple pendulum) and \( g \) (acceleration due to gravity), \( A \) = amplitude of S.H.M.

• A. \( A \sin \left( \sqrt{\frac{l}{g}} t \right) \)
• B. \( A \cos \left( \sqrt{\frac{g}{l}} t \right) \)
• C. \( A \cos \left( \sqrt{\frac{l}{g}} t \right) \)
• D. \( A \sin \left( \sqrt{\frac{g}{l}} t \right) \)

Hint:

In simple harmonic motion, the displacement is typically a cosine or sine function, depending on the initial conditions.

Answer 1

The Correct Option is B

Step 1: Equation for Simple Harmonic Motion.
The linear displacement \( x \) of a simple pendulum follows the equation: \[ x = A \cos \left( \sqrt{\frac{g}{l}} t \right) \] where \( A \) is the amplitude, \( g \) is the acceleration due to gravity, and \( l \) is the length of the pendulum. This equation represents the motion of a simple pendulum in simple harmonic motion (S.H.M.)
Step 2: Final Answer.
Thus, the correct expression for the linear displacement is \( A \cos \left( \sqrt{\frac{g}{l}} t \right) \).