Simple Harmonic Motion

In SHM, displacement is given by: Given, \( x = \frac{A}{2} \Rightarrow \frac{A}{2} = A \cos(\omega t) \Rightarrow \cos(\omega t) = \frac{1}{2} \Rightarrow \omega t = \frac{\pi}{3} \] Now,

Step 1: Recall the physical relationship
For a simple pendulum, the period is related to length by: where is acceleration due to gravity.
Step 2: Square both sides

Step 3: Recognize the equation form
This is of the form , where: - - - (constant)
Step 4: Determine graph characteristics
The equation represents: - A straight line - Passing through origin (0,0) - With slope
Step 5: Verify other options
(A) Parabola - Would require
(C) Hyperbola - Would require
(D) Horizontal line - Would mean is constant