Question

3. Write a program called VibratingSystem that does the following a. Takes the following as input i. Spring constant, k; ii. Mass under vibration, m; iii. Coefficient of viscous damping, c, iv. Initial position of the mass. xi, v. And initial velocity of the mass. vi b. If the values k or m are less than or equal to zero, ask for those variables again. c. Plot the results for t from 0 to 20 seconds with increments of.05 seconds i. Label the x axis displacement and the y axis time ii. The title of the plot should be one of Undamped Vibration". 'Overdamped Vibration", "Critically Damped Vibration" or "Underdamped Vibration" depending the values provided (compare c and cc) 4. Test your program with different Underdamped Vibration values of k. m. c. xl and vl. For example, if you run the program above with the following values, you will get the graph on the right 0.8 0.6 0.2 k 50 m 20 0.2 -0.4 -0.6 0 268 1D 12 16 18 20 Time

This two problems go together

Answer 1

MATLAB program:

prompt = 'Enter the value of spring constant';
k = input(prompt);
if k <= 0
prompt = 'Enter correct value of k again';
k = input(prompt);
end
prompt = 'Enter the value of mass';
m = input(prompt);
if m <= 0
prompt = 'Enter correct value of m again';
m = input(prompt);
end
prompt = 'Enter the value of coefficient of viscous damping';
c = input(prompt);
prompt = 'Enter the initial position';
x0 = input(prompt);
prompt = 'Enter the initial velocity';
v0 = input(prompt);
w_n = sqrt(k/m);
zeta = c/(2*sqrt(m*k));
t = 0:0.05:20;
if c == 0
x = x0 * cos(w_n .* t) + (v0/w_n)*sin(w_n.*t);
plot(t,x);
ylabel('Displacement');
xlabel('Time');
title('Undamped');
end
if zeta < 1
w_d = sqrt(1 - zeta^2)*w_n;
x = exp(-zeta*w_n.*t).*(x0*cos(w_d.*t) + ((v0+zeta*x0*w_n)/(w_d)).*sin(w_d.*t));
plot(t,x);
ylabel('Displacement');
xlabel('Time');
title('Underdamped');
  
elseif zeta == 1
x = (x0 + (v0 + zeta*w_n).*t).*exp(-w_n.*t);
plot(t,x);
ylabel('Displacement');
xlabel('Time');
title('Critically damped');
else
C1 = (xo*w_n*(zeta + sqrt(zeta^2 - 1)) + v0)/(2*w_n*sqrt(zeta^2-1));
C2 = ((-1)*xo*w_n*(zeta - sqrt(zeta^2 - 1)) - v0)/(2*w_n*sqrt(zeta^2-1));
x = C1*exp((-zeta + sqrt(zeta^2 - 1)*w_n.*t)) + C2*exp((-zeta - sqrt(zeta^2 - 1)*w_n.*t));
plot(t,x);
ylabel('Displacement');
xlabel('Time');
title('Overdamped');
end

OUTPUT:

Enter the value of spring constant50
Enter the value of mass20
Enter the value of coefficient of viscous damping10
Enter the initial position0.5
Enter the initial velocity1

0.8 Underdamped 0.6 0.4 0.2 -0.2 0.2 -0.4 0.6 0 268 10 12 14 16 18 20 Time