Topic: Theory of Machines / Vibrations
The acceleration of Simple Harmonic Motion of a pendulum is proportional to
- A. Length of pendulum
- B. Time period
- C. Angular velocity
- D. Displacement
Answer: D. Displacement
Explanation: Equation for simple harmonic motion $x = A \sin \omega t$. Velocity $V = \frac{dx}{dt} = A \omega \cos \omega t$. Acceleration $a = \frac{dv}{dt} = -A \omega^{2} \sin \omega t = -\omega^{2}x$. Thus, acceleration is proportional to displacement ($a \propto x$).