Chapter 7, Problem 1P

To determine

(a)

A user-defined MATLAB function for the given math function $y\left(x\right)=0.6x^3{e}^{-0.47x}+1.5x^2{e}^{-0.6x}$; the value of $y\left(-2\right)$ and $y\left(4\right)$ using this function. (Write the function such that $x$ can be a vector.)

Answer to Problem 1P

Solution:

The value of $y\left(-2\right)$ is $16.8487$ and $y\left(4\right)$ is $2.5434$.

Explanation of Solution

The given function is,

$y\left(x\right)=0.6x^3{e}^{-0.47x}+1.5x^2{e}^{-0.6x}$

Solve the above equation for $y\left(-2\right)$.

$\begin{array}{c}y\left(x\right)=0.6x^3{e}^{-0.47x}+1.5x^2{e}^{-0.6x}\\ y\left(-2\right)=0.6{\left(-2\right)}^3{e}^{-0.47\left(-2\right)}+1.5{\left(-2\right)}^2{e}^{-0.6\left(-2\right)}\\ =16.8487\end{array}$

Solve the above equation for $y\left(4\right)$.

$\begin{array}{c}y\left(x\right)=0.6x^3{e}^{-0.47x}+1.5x^2{e}^{-0.6x}\\ y\left(4\right)=0.6{\left(4\right)}^3{e}^{-0.47\left(4\right)}+1.5{\left(4\right)}^2{e}^{-0.6\left(4\right)}\\ =2.5434\end{array}$

Write the MATLAB code to determine the user-defined MATLAB function for the given math function $y\left(x\right)=0.6x^3{e}^{-0.47x}+1.5x^2{e}^{-0.6x}$ and calculate the value of $y\left(-2\right)$ and $y\left(4\right)$ using this function.

MATLAB Code:

Function file

function y = Chapter7_56830_7_1P(x)

y = (0.6.*x.*exp(-0.47.*x))+(1.5.*x.^2.*exp(-0.6.*x));

Script file

x = [-2 4];

y = Chapter7_56830_7_1P(x);

disp('The test values for y(x) are:')

disp(y)

Save the MATLAB script with name, Chapter7_56830_7_1Pa.m in the current folder. Execute the script by typing the script name at the command window to get the code to make a $\text{3-D}$ plot (shown in the figure) that shows the trajectory of the ball during the first five bounces in which the position of ball is given as a function of time and the velocities is given in the $x$ and $y$ direction.

Result:

Conclusion:

Therefore, the value of $y\left(-2\right)$ is $16.8487$ and $y\left(4\right)$ is $2.5434$.

To determine

(b)

To make:

A plot of the given function $y\left(x\right)$ for $-4\le x\le 8$.

Answer to Problem 1P

Solution:

The program is stated as follows.

Explanation of Solution

The given function is,

$y\left(x\right)=0.6x^3{e}^{-0.47x}+1.5x^2{e}^{-0.6x}$

Write the MATLAB code to make a plot of the given function $y\left(x\right)$ for $-4\le x\le 8$.

MATLAB Code:

Function file

function y = Chapter7_56830_7_1P(x)

y = (0.6.*x.*exp(-0.47.*x))+(1.5.*x.^2.*exp(-0.6.*x));

Script file

x = -4:.1:8;

plot(x,Chapter7_56830_7_1P(x));

title('y(x) = (0.6.*x.*exp(-0.47.*x))+(1.5.*x.^2.*exp(-0.6.*x))')

xlabel('x-->')

ylabel('y-->')

Save the MATLAB script with name, Chapter7_56830_7_1Pb.m in the current folder. Execute the script by typing the script name at the command window to get the code to make a plot of the given function $y\left(x\right)$ for $-4\le x\le 8$.

Result:

Conclusion:

Therefore, the required program is stated above.