Spring mass system subjected to impulse excitation

function [f] = impulse(t,x,h,i)

mu=0.2; wn = 17.1552;

tspan = 0:0.01:1.35;

h = [1 zeros(1,135)];

for i = 1 : length(tspan)

% h(i) = 0 ;

% h(1) = 1 ;

% % hh(i)= 0 + h(i);

% The output is 1 only if the input is 0

% if tspan == 0

% h(i) = 0;

% end

f=zeros(2,1);

f(2) = x(2);

f(1)= -mu*9.81*sign(x(2)) - (wn^2)*x(1) + h(i) ;

end

end

the main problem is the value h(i) is not subtituting in 'f' equation.

The Script file for the above function file is -----

clear all

clc;

clf;

tic;

mu = 0.2;

wn = 17.1552;

tspan=0:0.01:1.35;

x0=[0;0];

[t,x]=ode45(@impulse,tspan,x0);

y = x(:,1);

ydot = x(:,2);

figure(1);

plot(t,y,'r','linewidth',2);

can some one please help me with code for the above equation of motion. I tried a lot but I coudn't finished. I am not good in matlab but this is needed very much. Around 15 days back I posted my code also but I coudn't follow the comments made by few people. Please help me.

[darova]

Please show you attempts

[Jim Riggs]

Also, a diagram defining terms is necessary.

[Karthik K]

function [f] = impulse(t,x,h,i)

mu=0.2; wn = 17.1552;

tspan = 0:0.01:1.35;

h = [1 zeros(1,135)];

for i = 1 : length(tspan)

% h(i) = 0 ;

% h(1) = 1 ;

% % hh(i)= 0 + h(i);

% The output is 1 only if the input is 0

% if tspan == 0

% h(i) = 0;

% end

f=zeros(2,1);

f(2) = x(2);

f(1)= -mu*9.81*sign(x(2)) - (wn^2)*x(1) + h(i) ;

end

end

the main problem is the value h(i) is not subtituting in 'f' equation.

Script file-------------

clear all

clc;

clf;

tic;

mu = 0.2;

wn = 17.1552;

tspan=0:0.01:1.35;

x0=[0;0];

[t,x]=ode45(@impulse,tspan,x0);

y = x(:,1);

ydot = x(:,2);

figure(1);

plot(t,y,'r','linewidth',2);

[darova]

Please explain what is h(i) ()

DOn't you forgot to divide the entire expression by m?

f(1)= -mu*9.81*sign(x(2)) - (wn^2)*x(1) + h(i) ;

[Karthik K]

h(i) is the output of the for loop, to create an array of [1 0 0 0 -----], it has to substitute the element of the array one by one with respect to 't' but it is only substituting the last element of the array.

Answer 1

[Bjorn Gustavsson]

You seem to have misunderstood how matlab integrates ODEs.

Your ODE-function, impulse, should return the derivatives, and , at time t. You put an unnecessary loop in there where you spend plenty of time doing mostly nothing. This is an example of an ODE for a falling body in with some drag:

function dxdtdvxdt = ode_falldrag(t,xv,C)
dxdtdvxdt(1) = xv(2); % dxdt = v, second component of vx
dxdtdvxdt(2) = -9.81 - C*vx(2)*abs(vx(2));
end

Then you can call it something like:

[t,x]=ode45(@(t,x) ode_falldrag(t,x,1.23),tspan,x0);

where I've arbitrarily chosen a random drag-coefficient.

As for how to model impulse, you have to do more of the work. I suggest that you take a look at approximating the Dirac-pulses with Gaussians with decreasing width.

HTH