How Do You Calculate the Kinetic Energy of a Stretched Spring?

[atri.shivam]

Homework Statement

A spring of mass m is pulled away from the centre from its two ends with a velocity v at a particular instant.Find its kinetic energy.

Homework Equations

KE=.5kx² is useless since k is not given but m is given
So i think i will have have to use .5mv²

The Attempt at a Solution

the velocity of the spring will gradually decrease and will become 0 at the centre.
if v(x) is the velocity at a particular distance from the centre then we can write
kinetic energy=1/2 m/l*dx*v(x)²(dx being a small distance x)
and then integrate to find KE.
i am unable to find v(x) as a function of x.

 

[tiny-tim]

Welcome to PF!

if v(x) is the velocity at a particular distance from the centre then we can write
kinetic energy=1/2 m/l*dx*v(x)²(dx being a small distance x)
and then integrate to find KE.
i am unable to find v(x) as a function of x.

Hi atri.shivam! Welcome to PF!

v(x), at any particular time, will be proportional to x … that's how springs work!

(assuming there's no wave in the spring! )

 

[atri.shivam]

but what will be the equation of v(x)