Solution to the SDOF spring-mass-dashpot system subjected to a half-sine pulse

[Tunalover]

thread384-436025

I found the closed-form solution thanks to Tom Irvine. Such a simple model does have practical value IMO in studying the vertical responses of shock-mounted equipment subjected to shock pulses like those in MIL-STD-810 simulating transit drop and other collisions. I worked on the problem on and off for years then finally when I contacted Tom I learned I was solving the wrong problem all along (a 1/4-sine pulse...Duh!). Tom's well-documented solution is in the attached 29-page pdf. Surprisingly, I couldn't find a published solution anywhere else! It's an innocent looking ODE until you get into it and the math gets hairy, to put it mildly.

IMO knowing the transient response with damping may come in useful someday. Until then I'm going with the undamped response for design purposes since I'm normally concerned most with deflection and attenuated acceleration. It was an interesting exercise though that helped keep my math skills up to par.

ElectroMechanical Product Development
(Electronics Packaging)
UMD 1984
UCF 1993

 

[hacksaw]

Thesolution and methology of that class ofd problems is well known or at least it was in the 1960's, and a common topic in advance differential equations, for example

Louis Brand "Differential and Difference Equatons" 1966, Example 4 page 310.