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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

Accelerated mass and spring system

1. 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.

2. 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.