A body of mass m attached to one end of ...

A body of mass m attached to one end of an ideal spring of force constant k is executing simple harmonic motion. Establish that the time - period of oscillation is `T=2pisqrt(m//k)`.

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Derivation : Consider a body of mass m attached to one end B of a light elastic massless apring of spring constant k. The other end A of the spring is fixed to a rigid support. The body is resting on frictionless horizontal surface. The weight of body is balanced by the reaction of the horizontal surface.

Let the body be displaced towards right through a small distance y. The spring gets stretched. A restoring force F comes into play due to elastic nature of the spring.
`F=-"ky"`
In the displaced position if the body is left free.
It will start executing SHM on the smooth surface.
Here, inertia factor = mass of body (m)
Spring factor = force constant of spring = k
`:.` Periodic Time, `T=2pisqrt(("Inertia factor")/("Spring factor"))`
`=2pisqrt((m)/(k))`
`T=2pisqrt((m)/(k))`

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