PHY2061 R. D. Field Department of Physics chp36_11.doc University of Florida Another Differential Equation Consider the 2ndorderdifferential equation dxtdtDdx tCx t220()++=, where Cand Dare constants. We solve this equation by turning it into an algebraic equationby looking for a solution of the form xtAeat=. Substituting this into the differential equation yields, aDaC20=or aDDC=−±−222. Case I (C > (D/2)2, damped oscillations): For C > (D/2)2, iCDDi±−±′/(/)/22ω, where ′CD(/)22, and the most general solution has the form: eBeeAtBtttDtitDtcos()sin()s()s()////=+=′+′=′ +
This is the end of the preview. Sign up
access the rest of the document.