Engineering Maths and Modelling

Engineering Maths and Modelling

Table of Contents
Question 1...................................................................................................................................................3
Question 2...................................................................................................................................................5
Question 3...................................................................................................................................................6

Question 1
V(dx/dv) = -x
v.dv= -x dx
Initial value x=a, v=0, Put in equation 3,
V^2/2 = - x^2/2 + c
0 = -a^2/2 + c
C = a^2/2
X = a cos (t)^1/2
function yp = unforced1(t,y)
yp = [y(2);(-((c/m)*y(2))-((k/m)*y(1)))];
tspan=[0 4]; y0=[0.02;0];
[t,y]=ode45('unforced1',tspan,y0);
plot(t,y(:,1)); grid on xlabel(‘time’) ylabel(‘Displacement’) title(‘Displacement Vs Time’)
N = 200;
phi = pi/4;
A = 1;
B = 1;
t0 = -2;
tf = 2;
t = t0:(tf-t0)/(N-1):tf;
w = pi;
x = A*cos(w*t+phi);
y = B*cos(2*w*t-phi);
plot(t,x,'linewidth',3,'color','r')
grid
hold on
plot(t,y,'linewidth',3,'color','b')
a = title('Harmonic motion of phase \phi = \pi/4');
set(a,'fontsize',14);
a = ylabel('y(t), x(t)');
set(a,'Fontsize',14);
a = xlabel('t [-2 2]');
set(a,'Fontsize',14);
legend('x(t)', 'y(t)')