This calculator will determine the shock response to a dropped weight onto a spring and viscous damper. The spring and damper are mass-less and, therefore, the results are valid for both the case of 1) the spring/damper attached to the bottom of the weight and dropped onto a hard surface and 2) the rigid weight dropped onto the spring/damper. This version is limited to one vertical degree of freedom.
A limited number of time steps are used in the solution. For large drop heights, low damping and stiff springs the drop response will be multiple low damped bounces. For smaller drop heights, moderate to high damping (>10%) and soft springs (fn < 10-20 Hz) the drop response will be one to a few rebounds and will likely stop at the static deflection of W/k.
The chart shows the displacement response for spring/damper versus time. It also shows the acceleration as measured by an accelerometer attached to the dropped object. During free-fall the accelerometer would be 0.0. The maximum acceleration would normally occur during the first drop 1/2 cycle which corresponds to the maximum spring damper displacement.
For a verification check: with W=100 lbs, k=1000 lb/in, c=0, Vo = 0, G = 386.4 and h=1 inch. The maximum calculated spring displacement ∆ = 0.56 inches. The potential energy of the dropped object is W(h+∆) = (1+0.56) 100=156 in-lb. The energy of the compressed spring is 1/2k∆2 = ½ (1000) (.56)2=156 in-lb. Therefore, there is energy balance.
For further verification: if Vo=10 in/s is added to the previous conditions then the added kinetic energy is 1/2*(W/G) Vo2 = 1/2(100/386.4)(10)2 = 13 in-lb for a total energy of 172 in-lb. The calculated spring displacement is now 0.587 inches corresponding to a spring energy of 172 in-lb. There is energy balance for this condition as well.
