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Question: driven harmonic oscillator - amplitude & phase angle

Question:driven harmonic oscillator - amplitude & phase angle

longrob 1404 Maple
student
February 01 2010
0
Hi all I'm trying to obtain an expression for oscillatory motion in terms of the long-run amplitude, phase angle and frequency of a driven oscillatory system: deq:=diff(x(t),t$2)+lambda*diff(x(t),t)+omega[0]^2*x(t)=F[0]*sin(omega*t); The steady state solution I get from Maple is in this form ss:=((-omega[0]^2+omega^2)*sin(omega*t)+cos(omega*t)*omega*lambda)*F[0]/(omega^4+(lambda^2-2*omega[0]^2)*omega^2+omega[0]^4); How can I persuade Maple to manipulate this into the more usual A*sin(omega*t+P) where A is 1/sqrt(omega^4+(lambda^2-2*omega[0]^2)*omega^2+omega[0]^4) and P is arctan(omega/(1-omega^2); I tried siderels:=s=arctan(lambda*omega/(omega[0]^2-omega^2)); assume(omega>0); simplify(ss,{siderels}); Thanks LR
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