# Time period of a SPRING

time period of a "SPRING"

## Homework Statement

A spring has mass is m and natural length "L" and spring constant "k" has its one end fixed and the other end stretched by a length "a" and released.What is the time period of its oscillations?(there is no other mass attached to the spring,only the spring has mass m distributed uniformly across its length)

## Homework Equations

Kx=ma
Energy of a stretched spring = 1/2kx^2+(kinetic energy)

## The Attempt at a Solution

The net energy possessed by the system is constant(E).This energy exists in the form of kinetic and potential energy.
E=1/2(kx^2)+ kinetic energy

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## Homework Statement

A spring has mass is m and natural length "L" and spring constant "k" has its one end fixed and the other end stretched by a length "a" and released.What is the time period of its oscillations?(there is no other mass attached to the spring,only the spring has mass m distributed uniformly across its length)

## Homework Equations

Kx=ma
Energy of a stretched spring = 1/2kx^2+(kinetic energy)

## The Attempt at a Solution

The net energy possessed by the system is constant(E).This energy exists in the form of kinetic and potential energy.
E=1/2(kx^2)+ kinetic energy

I don't have any idea
I wanted to write the energy equation and defferentiate it with respect to time but I couldn't get the kinetic energy of the spring and relate it with x

rude man
Homework Helper
Gold Member
A spring with mass is not an easy thing to analyze. Look for something on the Web.

haruspex