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Spring-Mass System — Definition

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Version 1Updated 22 Mar 2026

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Definition

Imagine you have a simple setup: a block of a certain mass connected to a spring. One end of the spring is fixed to a wall, and the block is free to move on a smooth, frictionless surface. This entire arrangement is what we call a spring-mass system.

When the block is at rest, the spring is neither stretched nor compressed; this is its natural length, and the block's position here is called the equilibrium position. Now, if you pull the block a little bit to the right and then let it go, what happens?

The spring, being stretched, tries to pull the block back towards its original, equilibrium position. This pull is a 'restoring force'. As the block moves back, it gains speed. When it reaches the equilibrium position, the spring is at its natural length, so the restoring force momentarily becomes zero.

However, due to its inertia, the block doesn't stop; it overshoots the equilibrium position and starts compressing the spring. Now, the compressed spring pushes the block back towards the equilibrium position.

This push is again a restoring force, but this time acting in the opposite direction. The block slows down, momentarily stops at some point to the left, and then starts moving back towards the right, repeating the entire cycle.

This back-and-forth motion is called oscillation. The key characteristic of this oscillation, under ideal conditions (no friction, massless spring), is that it's a special type of periodic motion called Simple Harmonic Motion (SHM).

In SHM, the restoring force is directly proportional to the displacement from the equilibrium position and always acts in the direction opposite to the displacement. This relationship is described by Hooke's Law.

The time it takes for one complete back-and-forth cycle is called the time period, and the number of cycles per second is the frequency. Understanding the spring-mass system is fundamental because it provides a clear, tangible example of SHM, a concept that underpins many phenomena in physics, from sound waves to atomic vibrations.