Deriving the Equation for Spring Deflection of a Dropped Mass

[rotin089]

i have the following question and i have no idea how to answer it can any please help out...

consider a Mass M which is dropped a height z onto a spring of stiffness k N/m. when the mass hits the spring, the spring will deflect a distance x before the mass stops moving down. show that the distance x is a function of the mass M, acceleration due to gravity g and of stiffness of the spring k.

please help

 

[Doc Al]

Hint: Is anything conserved?

 

[rotin089]

energy both pe and ke

 

[Doc Al]

energy both pe and ke

The total mechanical energy is conserved. Use that to set up an energy equation to solve for X.

 

[rotin089]

i do not need to solve the equation. i need to find the derivative of the equation. i need to conclude that x is a function of the mass M, acceleration due to gravity g and of stiffness of the spring k.

 

[Doc Al]

i do not need to solve the equation. i need to find the derivative of the equation. i need to conclude that x is a function of the mass M, acceleration due to gravity g and of stiffness of the spring k.

Set up the energy balance equation--which will involve x, z, M, g, and k--then you can rearrange to get x as a function of the other parameters. (That's what I mean by 'solving for x'.)