State the conditions under which a body must travel if it is to move with simple harmonicmotion

A body will move in Simple Harmonic Motion (SHM) under the following conditions:

1. The force acting on the body is directly proportional to the displacement from its equilibrium position. This means that the further the body moves from its equilibrium position, the greater the force that tries to restore it back to that position.

2. The force is always directed towards the equilibrium position. This means that the force always tries to bring the body back to its equilibrium position.

3. The body's acceleration is directly proportional to its displacement but in the opposite direction. This means that the faster the body moves away from its equilibrium position, the faster it tries to return.

4. The motion is periodic, meaning it repeats itself after regular intervals of time.

5. The body's velocity and acceleration are 90 degrees out of phase. This means that when the body is at the maximum displacement (either positive or negative), its velocity is zero but its acceleration is at a maximum. Conversely, when the body is at the equilibrium position, its velocity is at a maximum but its acceleration is zero.

6. The body's kinetic and potential energies are constantly interchanging, but the total energy remains constant. This is due to the conservation of energy.