± Introduction to Simple Harmonic Motion Consider the system shown in the figure

Question

± Introduction to Simple Harmonic Motion Consider the system shown in the figure.(Fiqure 1) It consists of a block of mass m attached to a spring of negligible mass and force constant k The block is free to move on a frictionless horizontal surface, while the left end of the spring is held fixed. When the spring is neither compressed nor stretched, the block is in equilibrium. If the spring is stretched, the block is displaced to the right and when it is released, a force acts on it to pull it back toward equilibrium. By the time the block has returned to the equilibrium position, it has picked up some kinetic energy, so it overshoots, stopping somewhere on the other side, where it is again pulled back toward equilibrium. As a result, the block moves back and forth from one side of the equilibrium position to the other, undergoing oscillations. Since we are ignoring friction (a good approximation to many cases), the mechanical energy of the system is conserved and the oscillations repeat themselves over and over Figure 1 of 2

Explanation / Answer

Part A

We know that by hooke's law, spring force is directly proptional to the extension or coompression in the spring

So here restoring force is spring force only, So restoring force will be directly proptional to the displacment of the block.

Part B

When the block is at a distance A from the equilibiruim position, the spring force acting will be

kA

So by newton's second law F=ma

SO,

kA=ma

a=kA/m

Part C

When it passes through eqilibirium position, the extension or compression will be zero, So no spring force will be acting , So no acceleration.

Hence zero acceleration.

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