ENED 1090: Engineering Models I Homework Assignment #4 Due: Week of October 7 th at the beginning of your Recitation Section

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1 ENED 1090: Engineering Models I Homework Assignment #4 Due: Week of October 7 th at the beginning of your Recitation Section Instructions: 1. Before you begin editing this document, you must save this document to your laptop or you will end up losing all of your work. If you opened this document directly from Blackboard, click on the Enable Editing button then choose File Save As and save the document to your laptop. You should set up a folder on your laptop for ENED1090 where you keep all of your homework assignments and lab reports. 2. Show your work! 3. It is fine to work with other students, but what you turn in must be your own work - not something copied from someone else. Problem 1: The table below shows the velocity of an object in increments of 0.5 seconds. t (seconds) velocity (cm/s) (a) Using the data provided, estimate the velocity of the object at seconds using nearest point interpolation. 10 (b) Using the data provided estimate the velocity of the object at seconds using linear interpolation. Do this part by hand (don t use interp1) and show your calculations. ( )/(1-.5) = 1.5x *( )= (c) Suppose we wish to insert 3 new data points (evenly spaced in time, t) between each adjacent set of points in the table. What would the new increment for t be?.125 (d) Calculate the three new data points between t = 0.5 and t = 1.0 in the table below using linear interpolation. OK to use interp1 for this. Show your calculations or MATLAB command to get these three points. t velocity (cm/s)

2 yint=interp1([ ],[ ],0.625, linear ) yint= yint=interp1([ ],[ ],0.750,'linear') yint = yint=interp1([ ],[ ],0.875,'linear') yint = Problem 2: The graph on the following page shows the position of an object in increments of 0.5 seconds. (a) Using linear interpolation, estimate the position of the object at 6.85 seconds. Do this by hand (no interp1) and show your calculations. (4-7)/(7-6.5)= -6x 7+(-6)*( ) = 4.9 (b) Now use interp1 and linear interpolation to estimate the position of the object at 6.6, 6.7, 6.8, and 6.9 seconds , , , MATLAB Command and Results: >>yint=interp1([ ],[7 4],6.6,'linear') yint = >> yint=interp1([ ],[7 4],6.7,'linear') yint = >> yint=interp1([ ],[7 4],6.8,'linear') yint = >> yint=interp1([ ],[7 4],6.9,'linear') yint =

3 Problem 3: For this problem, you need the excel file, HW4_PB3.xlsx posted on the Blackboard metasite under Assignments, HW#4. The excel file has a vector of times, Time, which starts at 0 increments by 0.05 and ends at 1 second. It also has a vector of voltage measurements, Voltage, corresponding to the given times. Import both columns into MATLAB using the import tool or the xlsread command. (a) Use interp1 with a method of nearest to estimate the voltage every seconds between 0 and 1 second. On the same plot (not subplot), plot the original data points as red circles and the interpolated data points as black points. MATLAB Commands and Plot %Homework 4--Problem 3; %Alex Sullivan-- November 2, 2016 data=xlsread( HW4_data.xlsx','A2:B22'); time=data(:,1); voltage=data(:,2); tint=0:.001:1; yint=interp1(time,voltage,tint,'nearest'); plot(tint,yint, k.',time,voltage,'ro'); xlabel('time');ylabel('voltage'); title('interpolation: Nearest );

4 (b) Use interp1 with a method of linear to estimate the voltage every seconds between 0 and 1 second. On the same plot (not subplot), plot the original data points as red circles and the interpolated data points as black points. MATLAB Commands and Plot

5 %Homework 4--Problem 3; %Alex Sullivan-- November 2, 2016 data=xlsread( HW4_data.xlsx','A2:B22'); time=data(:,1); voltage=data(:,2); tint=0:.001:1; yint=interp1(time,voltage,tint,'linear'); plot(tint,yint, k.',time,voltage,'ro'); xlabel( time');ylabel('voltage'); title('interpolation: Linear'); (c) Use interp1 with a method of spline to estimate the voltage every seconds between 0 and 1 second. On the same plot (not subplot), plot the original data points as red circles and the interpolated data points as black points. MATLAB Commands and Plot

6 %Homework 4--Problem 3; %Alex Sullivan-- November 2,2016 data=xlsread( HW4_data.xlsx','A2:B22'); time=data(:,1); voltage=data(:,2); tint=0:.001:1; yint=interp1(time,voltage,tint,'spline'); plot(tint,yint, k.',time,voltage,'ro'); xlabel('time');ylabel('voltage'); title('interpolation: Spline ); (d) What kind of waveform does your plot in part (c) look like? Could you possibly have picked this up from looking at the original data points? It represents a sine curve. Yes, when the data points went from -1, to very close to zero, then to 1, I could tell that it would produce a harmonic motion, or a sine curve. Problem 4: Do the following in a script file. You can then copy the commands from your script file and the resulting output into this document. (a) Write a set of input statements that prompt the user for the year, month (a string), and the day that he/she was born. %Homework 4, Input Statements; %Alex Sullivan, November 2nd, 2016 month=input('what month were you born?(name):', s'); day=input('what day of the month were you born(xx) : '); year=input('what year were you born(xxxx)? : ); fprintf('birthday is %s,%i,%i',month,day,year); (b) Write a single fprintf statement that will display the user s birthday using the variables generated from your input statements. >> HW4_problem4 What month were you born?(name): July What day of the month were you born(xx) : 10 What year were you born(xxxx)? : 1999 Birthday is July,10,1999>>

7 Problem 5: Do the following in a script file. You can then copy the commands from your script file and the resulting output into this document. (a) Write a set of input statements that prompt the user for his/her favorite band, favorite song, favorite restaurant, and favorite food. %Homework 4, Input Statements; %Alex Sullivan, November 3rd, 2016 band=input('what is your favorite band?', s'); song=input('what is your favorite song?', 's'); restaraunt=input('what is your favorite restaraunt?', s'); food=input('what is your favorite food?', 's'); (b) Write two fprintf statements. The first statement should display the user s favorite band and favorite song. The second statement should display the user s favorite restaurant and favorite food on a new line. fprintf('favorite band is %s, and favorite song is %s\n,band,song); fprintf('favorite restaurant is %s, and favorite food is %s,restaurant,food); >> HW4_Problem5 What is your favorite band? Florida Georgia Line What is your favorite song? Play it Again What is your favorite restaurant? Outback What is your favorite food? Steak Favorite band is Florida Georgia Line,and favorite song is Play it Again Favorite restaurant is Outback, and favorite food is Steak>> Problem 6: Include your MATLAB statement and a screen shot of your pop-up menu. (a) Write a menu statement that instructs the user to choose one of the following interpolation schemes: Nearest, Linear, or Spline and saves the user s choice under the variable, Method. method=menu('interpolation Schemes','Nearest','Linear','Spline') (b) In part (a), what is the variable, Method, if the user chooses Linear? 2

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