Solving Underdamped Equation of motion

*To*: mathgroup at smc.vnet.net*Subject*: [mg6436] Solving Underdamped Equation of motion*From*: cliggio at aol.com (CLiggio)*Date*: Thu, 20 Mar 1997 00:52:45 -0500 (EST)*Organization*: AOL http://www.aol.com*Sender*: owner-wri-mathgroup at wolfram.com

I am trying to solve a differential equation. The equation is the equation of motion for a spring and dashpot. The solution is textbook. As an exercise I would like to obtain the same solution using Mathematica. The equation is: x''+ 2 z w x' + w^2 x = y'' where y'', the forcing function, is just a variable here. When mathematica solves it. It gives me a solution in the form of e to some exponent. The form I want it in is in aCosb + cSind. I used the ExpToTrig function but it gives me the equation in the form of Cosh and Sinh. In order to get the output to produce what I want, I have to tell Mathematica z is less than one. This corresponds to an underdamped system. If I enter a value of z <1 and then do the ExpToTrig function I get the solution I want. However it is evaluated at z = to that value and does not give me the general solution. Does anyone know how I can get it to produce the general solution for z < 1. In other words to constrain it at that set of values? The command I enter is below: z has been replaced with zeta, and with omega DSolve[{X''[t]+2* \[Zeta] *\[Omega]* X'[t]+\[Omega]^2*X[t]==-z},X[t],t] Thanks, Carl Liggio CLiggio at aol.com