Deriving the Equation for Spring Deflection of a Dropped Mass

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The discussion focuses on deriving the equation for spring deflection (x) when a mass (M) is dropped from a height (z) onto a spring with stiffness (k). It emphasizes the conservation of mechanical energy, where potential energy (PE) and kinetic energy (KE) are considered. Participants suggest setting up an energy balance equation that incorporates x, z, M, g (acceleration due to gravity), and k. The goal is to express x as a function of these parameters without solving the equation. Ultimately, the conclusion is that x depends on mass, gravitational acceleration, and spring stiffness.
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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
 
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Hint: Is anything conserved?
 
energy both pe and ke
 
rotin089 said:
energy both pe and ke
The total mechanical energy is conserved. Use that to set up an energy equation to solve for X.
 
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.
 
rotin089 said:
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'.)
 

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