Question

A body of mass 16 kg is oscillating on a spring of force constant 100 N/m.

1. What do you mean by spring constant.

2. Derive a general expression for period of oscillating spring.

Answer 1

1. Spring constant is the force required for unit extension.

2.

Consider a body of mass m attached to a massless spring of spring constant K. The other end of spring is connected to a rigid support as shown in figure. The body is placed on a frictionless horizontal surface.

If the body be displaced towards right through a small distance Y, a restoring force will be developed.

Comparing this equation with standard differential equation \(\frac{d^2x}{dt^2}\) + ω²x = 0

We get ω² = k/m