Small oscillation
Consider a simple pendulum (or a compass needle) undergoing small oscillation. Which one of the following statements is the more correct statement?
- The small oscillation is a rotational motion. A rotation is a rotation is a rotation.
The small oscillation is better thought of as a translational motion, whenever confusions ($\omega$ and $\dot{\theta}$) attack.
Ans: The intended answer is B. You might argue about it, and I am not going to take issues with that. However, my real message here is this. For a small angle motion (like what we are doing on the face of the earth every moment), it is often helpful to think of it as a translation. If you think that, then you may make less mistakes, like confusing $\omega$ with $\dot{\theta}$. Keep in mind that $\omega$ in a SHM solution is the angular frequency of the uniform circular motion in a complex plane, or a phase space, while $\dot{\theta}$ in a simple pendulum motion is not constant at all.