How Is Work Calculated for a Driver Plate During Stress Accumulation?

[onandon]

Show that the work done by the driver plate during a stress accumulation phase is W=$\frac{2m²g²f_d}{k}$(f_s-f_dI'm not sure where to start with this. I am given several equations but can't reach the desired equation.
F_n=ρghA
m=ρA^3/2
θ=$\frac{f_s}{f_d}$
X=$\frac{xG}{2f_sρghA^1/2}$
U=$\frac{u}{f_sgh}$($\frac{G}{2ρ}$)^1/2

Homework Statement

Homework Equations

The Attempt at a Solution

 

[member 553083]

The work done by the driver plate during a stress accumulation phase is given by W = Fs*X, where Fs is the force exerted by the driver plate and X is the displacement of the driver plate. Using the equations given, we can rewrite Fs as Fn/θ and X as U*(G/(2ρ))1/2. Therefore, we can calculate the work done during a stress accumulation phase as follows:W = \frac{Fn}{θ} * U * \frac{G}{2ρ})1/2= \frac{ρghA}{θ} * \frac{u}{fsgh} * \frac{G}{2ρ})1/2= \frac{2m2g2fd}{k}(fs-fd