The acceleration of a particle executing the simple harmonic motion is:

Where is angular velocity of a particle.
To find the answer of the above question if simple harmonic motion is there in the spring block system. If the SHM start with its mean position, so we can write the displacement equation as follows:

From above equation we find velocity equation

Now we multiply both by as shown

From the above equation, it's clearly given that force is directly proportional to negative of the displacement . So the Simple harmonic motion is constant in periodic time .

When both the mass and spring constant is constant there is no change in time period. The minimum time after which the particle keeps on repeating its motion is known as the time period. The formula of time period is:

Where is spring constant.