Question

(a) Use a computer program to plot the cycloid curve in the xy plane, given the parametric equations:

x(θ) = θ - sin θ

y(θ) = 1 - cosθ

(b) For a charge q moving in crossed (i.e., orthogonal) E and B fields, starting from rest at the origin, plot the kinetic energy as a function of time.

Answer 1

I have plotted it in MATLAB. Here is the code

clc;clear;

% patameter time or theta
t=[0:0.1:15];

% cycloid equations
x=t-sin(t);
y=1-cos(t);

% kinetic energy and time relation
KE=(sin(t./2)).^2;

% plot for cycloid
subplot(2,1,1);
plot(x,y,'r')
xlabel('x-axis')
ylabel('y-axis')

% plot for Kinetic energy
subplot(2,1,2);
plot(t,KE,'b')
xlabel('t (or \theta)')
ylabel('K.E.')

Here is the screenshot