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