Accelerated mass and spring system

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Homework Statement

Imagine a mass attached to a spring, equivalent to a vehicle suspension system, where the mass we are considering is the unsprung mass of the wheel/axle assembly. We are told the unsprung mass is given an instantaneous acceleration of 50m/s². We are given the spring constant of the suspension springs (k = 500kN/mm) and we are given the mass of the wheel/axle assembly (m = 200kg). The system is assumed to be undamped.

I am trying to find the force which is exerted by the spring upward onto the vehicle body.

Homework Equations

This is directly proportional to the compression of the spring but as I see it I just cannot make it work. Conservation of energy seems best suited, however I require the velocity of the wheel assembly (for ke = ½mv²) which I do not know. I have no time step increment with which to work out the velocity either.

The Attempt at a Solution

The acceleration of the wheel/axle assembly is specified in a load case. The problem as I see it is relating this acceleration to the deceleration caused by the spring. I am hopefully just missing something but this problem really has me stuck. If the spring weren’t there then the force on the vehicle body would be a simple F = ma where the acceleration is 50m/s² I think, but this is a much worse than real case.

The mass is accelerated (say +ve direction) at the 'start' of the action and is immediately deccelerated (-ve direction) by the spring. But how this relationship is expressed I can't fathom.

Any advice or views are appreciated, thank you.

 

[Mentz114]

What is the effect of an 'instantaneous' acceleration ? I don't what it means. Is it a constant acceleration that begins instantaneously ? If so the problem makes sense.
If it is applied for an instant, there won't be any effect.

I thnk you have to go with a constant force, which begins abruptly.