solve a base excited spring damper system with sinusoidal excitation.

Question

Reuben Salisbury 2020-4-6

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https://ww2.mathworks.cn/matlabcentral/answers/515798-solve-a-base-excited-spring-damper-system-with-sinusoidal-excitation

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I'm modelling a spring damper system governed by the equation of motion m*x''+c*x'+kx=ky+cy''.

y is the input y=Y0sin(wt),

x is the output (motion of the mass)

k=spring constant

c=damping coefficient

m=mass

I need velocity and displacement profiles for the mass as outputs.

clear
t=0:0.1:15;                                          %time peroid
Y0= input('wave amplitude ') ;                        %Wave amplitude
l= input('length of wave ') ;                        %length of the wave
u=input('speed of boat');                                                %Boat Velocity
w=u/l;                                               %frequency of wave
y=Y0*sin(w*t);                                       %wave height model
c=2*Dr*(k*m)^(0.5);                                  %Damping coefficient
Dr=0.5;                                              %Required Damping Ratio
k=17000;                                             %Spring Constant of suspension
m=100;
wn=(k/m)^0.5;
wd=wn*(1-Dr^2)^0.5;
                  
syms x(t)
ode=m*diff(x,t,2)+c*diff(x,t)+k*x==y+(2*Dr/wn)*diff(y,t);
xSol(t)=dsolve(ode);