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Chapter 4: Problem 1

Write the MATLAB statements required to calculate \(y(t)\) from the equation $$ y(t)= \begin{cases}-3 t^{2}+5 & t \geq 0 \\ 3 t^{2}+5 & t<0\end{cases} $$ for values of \(t\) between \(-9\) and 9 in steps of \(0.5\). Use loops and branches to perform this calculation.

Short Answer

Expert verified
Here is a summary of the MATLAB script to calculate the function y(t) using loops and branches: ```MATLAB t = -9:0.5:9; y = zeros(size(t)); for i = 1:length(t) if t(i) >= 0 y(i) = -3 * t(i)^2 + 5; else y(i) = 3 * t(i)^2 + 5; end end disp([t' y']); ```

Step by step solution

01

Initialize variables and create an array for 't'

First, create an array for 't' from -9 to 9 in steps of 0.5 and initialize an empty array for storing the 'y' values: ```MATLAB t = -9:0.5:9; y = zeros(size(t)); ```
02

Create a loop for iterating through the values of 't'

We will use a for loop to iterate through the values of t: ```MATLAB for i = 1:length(t) ```
03

Use branches (if-else) to calculate y(t) based on the condition of 't'

Inside the loop, use an if-else statement to check the condition of t and calculate y(t) accordingly: ```MATLAB if t(i) >= 0 y(i) = -3 * t(i)^2 + 5; else y(i) = 3 * t(i)^2 + 5; end ```
04

End the loop and display the results

Close the loop with 'end' and finally, display the results (optional): ```MATLAB end disp([t' y']); ``` Putting it all together, here is the complete MATLAB script: ```MATLAB % Step 1: Initialize variables and create an array for 't' t = -9:0.5:9; y = zeros(size(t)); % Step 2: Looping through the values of 't' for i = 1:length(t) % Step 3: Calculate y(t) based on the condition of 't' if t(i) >= 0 y(i) = -3 * t(i)^2 + 5; else y(i) = 3 * t(i)^2 + 5; end % Step 4: End the loop and display the results end disp([t' y']); ```

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Most popular questions from this chapter

Write a MATLAB program to evaluate the function $$ y(x)=\ln \frac{1}{1-x} $$ for any user-specified value of \(x\), where In is the natural logarithm (logarithm to the base e). Write the program with a while loop, so that the program repeats the calculation for each legal value of \(x\) entered into the program. When an illegal value of \(x\) is entered, terminate the program. (Any \(x \geq 1\) is considered an illegal value.)

Current Through a Diode. The current flowing through the semiconductor diode shown in Figure \(4.4\) is given by the equation $$ i_{\theta}=l_{e}\left(e^{\frac{w_{3}}{1 T}}-1\right) $$ where $$ \begin{aligned} &i_{D}=\text { the voltage across the diode, in volts } \\ &v_{n}=\text { the current flow through the diode, in amps } \\ &I_{e}=\text { the leakage current of the diode, in amps } \\ &q=\text { the charge on an electron, } 1.602 \times 10^{-19} \text { coulombs } \\ &k=\text { Boltzmann's constant, } 1.38 \times 10^{-23} \text { joule/K } \\ &T=\text { temperature, in kelvins }(\mathrm{K}) \end{aligned} $$ The leakage current \(I_{o}\) of the diode is \(2.0 \mu \mathrm{A}\). Write a program to calculate the current flowing through this diode for all voltages from \(-1.0 \mathrm{~V}\) to \(+0.6 \mathrm{~V}\), in \(0.1 \mathrm{~V}\) steps. Repeat this process for the following temperatures: \(75^{\circ} \mathrm{F}, 100^{\circ} \mathrm{F}\), and \(125^{\circ} \mathrm{F}\), Create a plot of the current as a function of applied voltage, with the curves for the three different temperatures appearing as different colors.

How can a numerical array be made to behave as a logical mask for vector operations? How can the logical attribute be removed from a numeric array?

Program 1sgfit from Example \(4.7\) required the user to specify the number of input data points before entering the values. Modify the program so that it reads an arbitrary number of data values using a while loop and stops reading input values when the user presses the Enter key without typing any values. Test your program using the same two data sets that were used in Example 4,7. (Hint: The input function returns an empty array (1) if a user presses Enter without supplying any data. You can use function isempty to test for an empty array and stop reading data when one is detected.)

Tension on a Cable. A 200-pound object is to be hung from the cnd of a rigid 8 -foot horizontal pole of negligible weight, as shown in Figure 4.5. The pole is attached to a wall by a pivor and is supported by an 8 -foot cable that is attached to the wall at a higher point. The tension os this cable is given by the equation $$ T=\frac{W+k c \cdot l p}{d \sqrt{l p^{2}-d^{2}}} $$ where \(T\) is the tension on the cable, \(W\) is the weight of the object. Ic is the length of the cable, Ip is the length of the pole, and \(d\) is the distance along the pole at which the cable is attached. Write a program to determine the distance \(d\) at which to attach the cable to the pole to minimize the tension on the cable. To do this, the program should calculate the tension on the cable at regular l-foot intervals from \(d=1\) foot to \(d=7\) fect. and should locate the position \(d\) that produces the minimum tens on. Also, the program should plot the tension on the cable as a function of \(d\), with appropriate tities and axis labels.
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