The negative sign shows that the restoring force is always opposite to the distance. That is, when x is positive, F is negative, the force is tends to the left. When x is negative magnitude, F is positive magnitude; the force is directed to the right. So the force usually directed to restore the block to its equilibrium position x = 0.

                        F = -kx                                                                                                  ..... (i)

Applying Newton's Second equation,                                                  ..... (ii)

or        

Comparing the above equation with second order differential equation we get,

Note: The time period is independent of the amplitude. For a given spring constant, the period increases with the mass of the block -a more massive block oscillates more slowly. For a given block, the period decreases as k increases. A stiffer spring produces quicker oscillations.

COMBINATION OF SIMPLE HARMONIC MOTION:  

We have previously learnt about the simple harmonic motion of a body. A body may, sometimes, possess two or more simple harmonic motions simultaneously. Take the case of a simple pendulum suspended from a stand placed in a boat. If the bob of the pendulum is set into vibrations when the boat is tossing sideways, the bob is having its own S.H.M. and is also sharing the S.H.M. of the boat and moves at any moment in the direction of the resultant of these two motions. We shall now discuss the methods of finding the resultant of such simultaneous motions. Let us first take the case of two simple harmonic motions in the same direction when they have the same periodic time. Their resultant can be found either graphically or analytically. 

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