# What is the maximum kinetic energy in the following mass spring system:A 3.0 kilogram mass is attached to a spring having a spring constant of 30 N/m. The mass is pulled 0.20 meter from the...

What is the maximum kinetic energy in the following mass spring system:

A 3.0 kilogram mass is attached to a spring having a spring constant of 30 N/m. The mass is pulled 0.20 meter from the spring's equilibrium position and released.

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### 1 Answer

The sum of the kinetic energy and potential energy in a system is a constant. Only the form of the energy changes.

For a spring with a spring constant of 30 N/m, the energy stored is equal to (1/2)*k*x^2 where x is the distance by which the spring is compressed or extended from its equilibrium position.

Here we have the mass attached to the spring given as 3 kilogram and the spring is pulled by 0.2 m from its equilibrium position.

Initially, the sum of the kinetic and potential energy in the system is KE + PE = 0 + (1/2)*30*0.2^2

=> 0 + 0.6

When the spring returns to its equilibrium position all the energy is in the form of kinetic energy and the potential energy is 0.

**Therefore the maximum kinetic energy in the system is 0.6 J.**