Question

How is the motion of the mass on the spring similar to the motion of the bob? How is it different? Then, why does the period of a pendulum not depend on mass but it does for the spring? Explain carefully. Simple harmonic motion is used to describe physics most complex theories. How could something so simple describe the most complex

Answer 1

The period of a pendulum does not depend on mass but it does for a spring, because oscillations of simple pendulum occurs under the gravitational acceleration, which is not depending on the mass suspended. On the other hand, extension and compression of spring which depends on the mass attached to it.

The simple pendulum has no dependence on mass because the mass gets to "count" for two different things.

1. Mass counts for inertia or the "m" in "F=ma". That means, the resistance to changes in motion is directly proportional to the mass.

2. The weight (a force) on an object is also proportional to mass. Since, the mass factors into both the cause of changing motion & the resistance to changing motion, which it cancels out.

For a mass-spring system, the mass still affects the inertia but it does not cause the force. The spring (and its spring constant) is fully responsible for force. So, mass only impacts the resistance to accelerations.