Chapter 10, Problem 1P

To determine

To plot:

The position of a moving particle as a function of time from the equation, $x=\left[\frac{\left(t-15\right)}{100}+1\right]\sin \left(3t\right)$, $y=\left[\frac{\left(t-15\right)}{100}+1\right]\cos \left(0.8t\right)$ and $z=0.4t^{\frac{3}{2}}$ for $0\le t\le 30\text{}\text{s}$.

Answer to Problem 1P

Solution:

The program is stated as follows.

Explanation of Solution

The given equation is,

$x=\left[\frac{\left(t-15\right)}{100}+1\right]\sin \left(3t\right)$

$y=\left[\frac{\left(t-15\right)}{100}+1\right]\cos \left(0.8t\right)$

$z=0.4t^{\frac{3}{2}}$

The range of $t$ is $0\le t\le 30\text{}\text{s}$.

Write the MATLAB code to plot the position of a moving particle as a function of time from the equation, $x=\left[\frac{\left(t-15\right)}{100}+1\right]\sin \left(3t\right)$, $y=\left[\frac{\left(t-15\right)}{100}+1\right]\cos \left(0.8t\right)$ and $z=0.4t^{\frac{3}{2}}$ for $0\le t\le 30\text{}\text{s}$.

MATLAB Code:

t = 0:0.1:30;

%Define the variable t.

x = [((t-15)./100)+1].*sin(3.*t);

%Define the variable x.

y = [((t-15)./100)+1].*cos(0.8.*t);

%Define the variable y.

z = 0.4.*t.^(3/2);

%Define the variable z.

plot3(x,y,z,'r','linewidth',2)

grid on

xlabel('x'); ylabel('y'); zlabel('z')

Save the MATLAB script with the name, Chapter10_29864_10_1P.m in the current folder. Execute the script by typing the script name at the command window to get the code that plots the position of a moving particle as a function of time from the equation, $x=\left[\frac{\left(t-15\right)}{100}+1\right]\sin \left(3t\right)$, $y=\left[\frac{\left(t-15\right)}{100}+1\right]\cos \left(0.8t\right)$ and $z=0.4t^{\frac{3}{2}}$ for $0\le t\le 30\text{}\text{s}$.

Result:

Conclusion:

Therefore, the program is stated above.