Name: ____________________________ NetID: _________________ Section#: ______
1. Using the built-in function fzero write the Matlab command(s) to find a root of the function
y=x7- ln4(x)
with an initial guess of x= 5. (Don't write the
root 0.6359 approx.)
_____________________________________________________________
2. Using the built-in function fplot write the Matlab command to plot the function
y=x4 - ln4(x) on the interval [1,2].
____________________________________________________________
3. Using the built-in function quadl write the Matlab command to compute the definite integral of the function
on the interval [1,5]. (Don't write the answer 15.3662. Just the Matlab code that gives the answer.)
____________________________________________________________
4. Using the built-in function trapz write the Matlab command to compute the definite integral of the function
the interval [1,5] using 100 points. (Don't write the answer 15.3660. Just the Matlab
code that gives the answer.) You may use multiple lines.
x = __________________________________________________________
y =
__________________________________________________________
trapz( ____________________________ ,
________________________________)
5. Complete the following Matlab code, by filling in
the blanks, to plot the surface described by the equation,
z
= cos( sqrt(x2 + y2)) / sqrt(x2
+ y2)
over the interval [-10,10] x [-10,10] in the x-y plane.
>> y = x;
>> [XMAT, YMAT ] = meshgrid(x,y);
>> ZMAT = _________________________________________________________________________
>> surf( XMAT , YMAT , ZMAT )
6. We want to model the motion of a free falling object using the first order ordinary differential equation: http://en.wikipedia.org/wiki/Free_fall
(see also Classical Mechanics: A Modern Perspective 2nd ed. Barger and Olsson p. 8) where the mass of the object m = 75 Kg ,the acceleration due to gravity g = 9.8 m/s2 and
and
drag coefficient CD = 0.51, http://en.wikipedia.org/wiki/Drag_coefficient
cross-sectional area of the object, perpendicular to air flow A = 1.1 m2 ,
air density ρ = 1 Kg/ m3 ,
We want to solve for the vertical velocity v (which is a function of t written v = v(t) ) using the Matlab ODE solver ode45. Assume that at time t = 0, v = 0
( v(0) = 0).
To solve this equation we would type,
>> [ t,v] = ode45(@vprime, [0,100] , 0);
But we first need to complete the function named vprime.
a) Complete the function vprime by filling in the blank below.
function dv = vprime(t,v)
m = 75;
CD = 0.51;
A = 1.1;
rho = 1;
g = 9.8;
dv = ____________________________________________________________________________
b) Using this model what is the terminal velocity ? _____________________
(Hint: try plot(t,v) or v(end) )
Write the value that Matlab returns when you type the following at the command prompt:
>> x
x =
_____________________________
>> y
y =
_____________________________
>> result
result =
___________________________
Write the value that Matlab returns when you type the following at the command prompt:
>> result = dummy(-4)
result =
_____________________________
>> y = dummy(0)
y =
_____________________________
>> result
result =
___________________________
In the editor modify the code for the dummy function by adding the global command as shown below,
function result = dummy(parameter)
global x
x = 4;
result = x + parameter;
Write the value that Matlab returns when you type the following at
the command prompt:
>> global x
>> x
x =
_____________________________
>> y = dummy(-4)
y =
_____________________________
>> x
x =
___________________________
In the editor modify the code for the dummy function by removing the statement x =4; so that your function should now look like the following:
function result = dummy(parameter)
global x
result = x + parameter;
Write the value that Matlab returns when you type the following at
the command prompt:
>> x = 10;
>> y = dummy(-4)
y =
_____________________________
If the sound has been recorded backwards then let's solve the
problem of understanding the mystery message. Specifically,
the problem is that if
volts = [v1 v2 v3 ... vn] then we actually want [ vn ... v3 v2
v1]. Fill in the blanks and then type in this command to
listen to the message.
>> flipvolts = volts( _________ : _________ :
__________);
>> message = audioplayer(flipvolts,frequency);
>> play(message)
What is the mystery message that with enlighten mankind?
_____________________________________________________________________________________________
Write the command to display the number of values the vector flipvolts contains, (don't use size, that's for matrices)
>> __________________________________
Fill in the blank below with the new vector which is the old sound + new sound. You should hear the echo effect.
>> player = audioplayer(
(_______________________________)/peak , frequency);
>> play(player)
Fill in the blank to complete the code for the function named
Derivatives_resistance .
dydv =
_________________________________________________________
What is the time (in seconds approximately) when the object
hits the ground (y = 0) ? Hint: plot t versus y. Use grid on
command too.
t = _________________________________________________
(approx.)
What is the velocity ( meters/second approximately) when the
object hits the ground (y = 0)?
v = _________________________________________________(approx.)
(Of course this is the same answer as in prelab 5 question 6b)
Increase A (area) in the function named
Derivatives_resistance so that the terminal velocity is about
-10 meters/second. Round answer to nearest integer value.
A = ______________________________________________________
Complete the function named xyzprime that will compute the derivatives of the three dependent variables x, y and z , by filling in the blanks.
function dxdydz = Derivatives_xyz(t , xyz)
x = xyz(1);
y = xyz(2);
z = xyz(3);
dxdydz = [ ______________________________;
_________________________________ ;
___________________________________];
The actual data points (x,y,z) are plotted using A) squares
B) stars
C) circles
D) diamonds