What conditions are required for an object to undergo SHM?

An object undergoes Simple Harmonic Motion (SHM) when it experiences a restoring force proportional to its displacement and directed towards its equilibrium position.

Simple Harmonic Motion (SHM) is a special type of oscillatory motion where the restoring force acting on the object is directly proportional to its displacement from the equilibrium position and is always directed towards it. This means that the object will always be pulled or pushed back towards the point of equilibrium. The motion is termed 'simple' because it follows a simple, predictable pattern that can be easily analysed.

The first condition for SHM is that the object must be displaced from its equilibrium position. The equilibrium position is the point where the object naturally wants to rest, where all forces acting on it are balanced. When the object is displaced from this position, it experiences a restoring force.

The second condition is that the restoring force must be proportional to the displacement. This means that the further the object is from the equilibrium position, the stronger the force pulling or pushing it back. This relationship is often represented by the equation F = -kx, where F is the restoring force, k is a constant that depends on the properties of the system, and x is the displacement from the equilibrium position. The negative sign indicates that the force is always directed towards the equilibrium position.

The third condition is that the restoring force must always act towards the equilibrium position. This means that if the object is displaced to the left of the equilibrium position, the force will act to the right, and vice versa. This ensures that the object will oscillate back and forth around the equilibrium position.

In addition to these conditions, for an object to undergo SHM, the system must not lose energy to friction or other forms of energy dissipation. In reality, this is rarely the case, and most systems will gradually lose energy and come to a stop. However, in an idealised SHM system, the motion will continue indefinitely.