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);
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