Chapter 10, Problem 1P

To determine

To plot:

The position of a moving particle as a function of time from the equation,

$x=0.01{\left(30-t\right)}^2\sin \left(2t\right)$ ,

$y=0.01{\left(30-t\right)}^2\cos \left(2t\right)$ ,

and $z=0.5t^{1.5}$ for $0\le t\le 20\text{}\text{s}$ .

Answer to Problem 1P

Solution:

The program is stated as follows.

Explanation of Solution

The given equation is,

$x=0.01{\left(30-t\right)}^2\sin \left(2t\right)$

$y=0.01{\left(30-t\right)}^2\cos \left(2t\right)$

$z=0.5t^{1.5}$

The range of $t$ is $0\le t\le 20\text{}\text{s}$.

Write the MATLAB code to plot the position of a moving particle as a function of time from the equation,

$x=0.01{\left(30-t\right)}^2\sin \left(2t\right)$,

$y=0.01{\left(30-t\right)}^2\cos \left(2t\right)$,

and $z=0.5t^{1.5}$ for $0\le t\le 20\text{}\text{s}$.

MATLAB Code:

t = 0:0.1:20;

r = 0.01.*(30-t).^2;

x = r.*sin(2.*t);

y = r.*cos(2.*t);

z = 0.5.*t.^(1.5);

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

grid on

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

Save the MATLAB script with name, Chapter10_56830_10_1P.m in the current folder. Execute the script by typing the script name at the command window to get the code to plot the position of a moving particle as a function of time from the equation, $x=0.01{\left(30-t\right)}^2\sin \left(2t\right)$,

$y=0.01{\left(30-t\right)}^2\cos \left(2t\right)$,

and $z=0.5t^{1.5}$ for $0\le t\le 20\text{}\text{s}$.

Result:

Conclusion:

Therefore, the required program is executed above.