If a spring with a spring constant k = 10 n/m is stretched from its equilibrium position by 0.1 m , and released, what would be the maximum kinetic energy at any time in its motion? neglect friction.

2 weeks ago, oh boy.

So we know k is 10 N/m and it is stretch 0.1m. 
For the conservation of energy, we know the mechanical energy in the system is constant, and we know the energy switches from potential elastic energy to kinetic energy. So we can solve for the maximum potential elastic energy, which should tell us the mechanical energy.

Since we are told it is stretch 0.1m and we are given the spring constant, we can solve for max potential elastic energy.

Mechanical energy = Max potential = 0.5kA^2

This gives us 0.5(10N/m)(0.1m)^2 = 0.05J

The maximum kinetic energy is when the potential elastic energy is zero, thus 0.05J would be the maximum kinetic energy.

Hope this helps!