Linear spring and non-linear spring

[talaroue]

Homework Statement

If a delicate istrument havng a mas of 5 kg is placed on a springof length L so tha its base just touches the undeformed spring and then inadvertly released from the position, determine the maximum deflection xm of the spring assuming (a) linear spring constant k=3000N/m (b) a hard, nonlinear spring, for which F=3000N/m(x+160x3)

Homework Equations

F=-k(dx)

The Attempt at a Solution

5*9.81/3000=16.35 mm this is half of the answer why is that?

Also can someone point me in te right direction for the nonlinear spring, that would be great.

 

[teachofphys]

Are you in a calc based physics class, or an algebra based class? And do you have an understanding of conservation of energy yet? Or just work = force x displacment?

 

[talaroue]

I understand all of the mentione above, I am in EGN3400 aka Dynamics. But this is a very basic problem.

 

[teachofphys]

To solve this particular problem... Work is force times displacement, and change in kinetic energy is equal to work. Think about the initial and final kinetic energies for the falling mass, and set that equal to the work done by the variable forces.