Quick questions on mechanical vibrations (desperate for help)

a)Use the same model as in first case but for c=0.2 and let the driving frequency be constant ωdr=4 with zero initial conditions. Plot the motion of the system and describe the motion.

b) Let the force be accelerating such that (F sin(5t^2 /1000)). Plot the response (for c=0.2) for each mass as function of angular frequency. Explain the result

I have already solved part a) and i am currently stuck at part B)

It requires me to plot the response for each mass as a function of angular frequency, does any one have any idea on how do I go about it?

I need to plot a Response curve however I only have managed to plot a single frequency curve right now.

How do i simulate the system for TIME DEPENDENT frequency?

My code is shown below:

function R =  myfunction()
global A B F Z I wdr
c=0.2;
mass=1:3;  % masses 
% loop for each mass 
R = cell(length(mass),1) ;  %Result 
for i = 1:length(mass)
    m = mass(i) ;
    k=100;
    c=0.2;
    F0=10;
    t0=0;
    t1=100;
    M=[m 0 0 ;0 m 0 ; 0 0 m];
    K=[2*k -k 0;-k 2*k -k;0 -k k];
    C=[2*c -c 0;-c 2*c -c;0 -c c];
    for t=t0:t1
        wdr=(5*t/1000)%driving frequency
        
    end
    f=[0 0 F0*sin(wdr*t)]';% Force vector
    A=M\K;
    B=M\C;
    F=M\f;
    Z=zeros(3); % Zero matrix
    I=eye(3); % Diagonal matrix
    x0=[0 0 0 0 0 0]'; % Initial conditions
    [t,x]=ode45('Fun1',[t0 t1],x0);
    R{i}=[t,x] ;
    plot(t,x(:,1),t,x(:,2));
    title(sprintf('mass = %s',num2str(m)))
    drawnow
end

Fun1:

%Fun1.m
function dx = dyn1(t,x)
global A B F Z I wdr
dx=zeros(6,1);
dx = [Z I;-A -B]*x+[[0 0 0]'; F]*sin(wdr*t);
end

Answer 1

[Steve Miller]

You could very easily model this system in Simscape and use the results of that simulation to check your equations and plots. This model is only one copy-and-paste away from the system you are trying to model: Double Mass-Spring-Damper in Simulink and Simscape

https://www.mathworks.com/help/simscape/ug/double-mass-spring-damper-in-simulink-and-simscape.html

--Steve