Question

The equation of motion for a compound pendulum is:

• A. $\ddot{\theta} + \frac{mgl}{I} \cos\theta = 0$
• B. $\ddot{\theta} + \frac{mgl}{I} \sin \theta = 0$
• C. $\ddot{\theta} - \frac{mg}{I} \cos \theta = 0$
• D. $\ddot{\theta} - \frac{mg}{I} \cos \theta = 0$

Hint:

For small angles, sin θ ≈ θ, simplifying the equation to a linear form for simple harmonic motion.

Answer 1

The Correct Option is B

For a compound pendulum, the equation of motion is given by:
\[I \ddot{\theta} + mgl \sin\theta = 0\]
where $I$ is the moment of inertia, $m$ is the mass, $g$ is the acceleration due to gravity, and $l$ is the distance from the pivot point. The equation uses $\sin\theta$ for small oscillations.