Simple Pendulum — Definition

Definition

Imagine you tie a small, heavy stone to one end of a very light thread and hang the other end of the thread from a fixed point, like a nail on a wall. If you pull the stone slightly to one side and let it go, it will swing back and forth. This setup is what we call a 'simple pendulum'.

Let's break down its components and behavior:

1
The Bob: — This is the small, heavy stone or any concentrated mass at the end of the string. In an ideal simple pendulum, we assume this mass is a 'point mass', meaning its entire mass is concentrated at a single point, and its size is negligible compared to the length of the string.
2
The String/Thread: — This is the connection between the bob and the fixed support. Ideally, we assume the string is 'massless' (its mass is so small it doesn't affect the motion) and 'inextensible' (it doesn't stretch or change length during the swing).
3
The Suspension Point: — This is the fixed point from which the string and bob hang. It's assumed to be frictionless, allowing the pendulum to swing freely.

When you displace the bob from its resting position (called the equilibrium position) and release it, gravity pulls it downwards. However, because it's constrained by the string, this gravitational force creates a 'restoring force' that tries to bring the bob back to its equilibrium position. As the bob swings past the equilibrium, its inertia carries it to the other side, and the restoring force again pulls it back. This continuous back-and-forth motion is called oscillation.

Crucially, for the simple pendulum to behave like a 'simple harmonic oscillator' – a system that undergoes Simple Harmonic Motion (SHM) – the angle of displacement from the vertical must be small. What does 'small' mean here?

Typically, it's an angle less than about $10^circ$ to $15^circ$. When the angle is small, the restoring force becomes directly proportional to the displacement, which is the defining characteristic of SHM.

In SHM, the oscillations are regular and repetitive, and the time it takes for one complete back-and-forth swing (called the 'time period') remains constant.

So, in essence, a simple pendulum is a fundamental model in physics that demonstrates oscillatory motion, and under specific conditions (small angles), it beautifully illustrates the principles of Simple Harmonic Motion, making it a cornerstone for understanding periodic phenomena.