Question

Plot the solution of the equation

6ẏ + y = f(t)

 

if f (t) = 0 for t + 0 and f(t) = 15 for t ≥ 0. The initial condition is y(0) = 7.

Answer 1

Program plan:

• To write a matlab code to plot the differential equation with the given conditions.

 

Program:

%**********************************************************

%A matlab code is written to plot the motion of a mass

%connected to a spring with viscous friction on the surface

%with the given condition.

%**********************************************************

%Declaration of function, File name :\'msd.m\'

function xdot = msd(t,x)

%Declaration of global variable

global c f k m

%Declaration of array

A = [0,1;-k/m,-c/m];

%Declaration of array

B = [0;1/m];

%Computes the value

xdot=A*x+B*f;

%End of function

end

%Declaration of variable

global c f k m

%Declaration of constant

m = 3;

%Declaration of constant

c = 18;

%Declaration of constant

k = 102;

%Declaration of constant

f = 10;

%Computes the vales of the function \'msd\'

[t, x] = ode23(\'msd\', [0, 2], [0, 0]);

%Plotting

plot(t,x(:,1)),

%Assigns text to x-axis

xlabel(\'t\'),

%Assigns text to y-axis

ylabel(\'y\')

 

Outtput:

 

%Output with different constants m=3,c=39 and k=120

%Output with different constants m=3,c=39 and k=120