MATLAB (10)

Mass-Spring-Damper System

General Solution

syms s x0 xp0 wn z;
Xs=(x0*(s+z*wn)+(xp0+z*wn*x0)/(wn*(sqrt(1-z^2)))*wn*sqrt(1- z^2))/((s+z*wn)^2+(wn*sqrt(1-z^2))^2)
U=ilaplace(Xs)

실행결과

Xs =
 
-(xp0 + x0*(s + wn*z) + wn*x0*z)/(wn^2*(z^2 - 1) - (s + wn*z)^2)
 
 
U =
 
x0*exp(-t*wn*z)*(cosh(t*wn*(z^2 - 1)^(1/2)) - (sinh(t*wn*(z^2 - 1)^(1/2))*(wn*z - (xp0 + 2*wn*x0*z)/x0))/(wn*(z^2 - 1)^(1/2)))

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Simulink