**Question7: Is there some connection between F and x in mass spring system? **

ANSWER

Yes, force **F** and displacement **x** are inter-related in a mass-spring system.

A mass-spring system is one in which a certain mass is connected to a spring. Under the action of gravity, the mass exerts a force on the spring which stretches it. The restoring force in the spring attracts the mass again and the mass is, thus, set in Simple Harmonic Motion.

Consider a body having mass ‘m’ attached to the spring on one end. The spring is placed on a smoothfrictionless surface. Suppose ‘k’ is the spring constant. When a certain force is applied to the body, the spring is elongated to displacement **x**. Applying Hook’s law,

This equation gives the relation between **F** and **x** in a spring mass system. It states that greater force produces greater displacement (extension) in the spring.

**Check your understanding**

(1) In a spring mass system, the maximum displacement from the equilibrium point is called

(a) Wavelength |
(b) Amplitude |
(c) Period |

(2) When x = A (amplitude), the acceleration is,

(a) Maximum and positive

(b) Maximum and negative

(c) Zer

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