Description
Q1. Write a function that finds the magnitude of the roots of an input polynomial and outputs
the magnitude of the roots that fall within a user specified range of values LOW and HIGH. The
input polynomial � is entered as a row vector of coefficients as shown in the example on pp.262-
3 of the textbook.
The polynomial � = −0.001�) + 0.051�, − 0.76�/ + 3.8� − 1.4 is entered as � =
[−0.001, 0.051, −0.76, 3.8, −1.4]. The magnitude of the roots are:
29.6177, 10.8776, 10.8776, 0.3995. Now suppose the range is given as say LOW=9 and
HIGH=11, then the second and third roots [10.8776, 10.8776] will be output.
ENEL101 Assignment 6 Page 2
Q2. Write a function that accepts the vector of data points � and ℎ as input arguments and
determines a linear equation in the form of � = �ℎ + � that best fits the data. Then output the
magnitude of the error between the data points and the linear regression curve, denoted by the
vector of �. Use the Matlab polyfit() and polyval() functions. The input arguments are
the boiling temperature of water � at various altitudes ℎ as in
� (meters) 0 608 1520 2280 3040 6384 7904
� (Celsius) 100.00 98.88 95.00 92.22 90.00 81.11 75.55
Q3. Write a function that accepts the vector of data points � and � as input arguments and
determines the best exponential equation in the form of � = ��BC that best fits the data, using
the Matlab polyfit() function. Then output 1×2 vector � � . The input arguments are the
number of bacteria � measured at different times � as
� (min) 10 20 30 40 50
� 38,000 60,000 250,000 500,000 1000,000
Q4. Write a function named that accepts the integration limits of � and � as input arguments
and outputs the integral of ( ) 2 3 hx x x x ( ) sin( )exp = – . Use the Matlab quad() function for this.
That is the function does the following
( ) 2 3 sin( ) exp
B
A
Z x x x dx = – ò
Q5. The following wind tunnel data shows the aerodynamic drag force on a car, �I, as a
function of the car velocity, �.
v km hr ( /) 20 40 60 80 100 120 140 160
F N D ( ) 10 50 109 180 300 420 565 771
Write a function that accepts an arbitrary value for v and output the corresponding interpolated
value of FD . Use Matlab function interp1() with the ‘spline’ method for the interpolation.
ENEL101 Assignment 6 Page 3
Q6. An RLC circuit with an alternating voltage source is assumed. The source voltage �K is
given by �K = �Bsin (�Q�), where �Q = 2��Q in which �Q is the driving frequency. The
normalized amplitude of the current, �, in this circuit is given by
� = 1
�/ + �Q� − 1
�Q�
/
where � (Ω), � (H), and � (F) are the resistance of the resistor, the capacitance of the capacitor,
and the inductance of the inductor, respectively. Write a function named that accepts �, �, and �
as input arguments and finds the natural frequency of the circuit (the frequency at which � is
maximum). The natural frequency of �Z (Hz) is the output argument. Use Matlab’s
fminbnd() for this application and search over 0.5/ �� < �Q < 1.5/ ��. Note that
minimizing −� is equivalent to maximizing �.
Q7. The sudden outbreak of an insect population can be modelled by the equation
� �
� � = �� 1 − �
� − � �/
�_
/ + �/
where � is the number of insects, � is an intrinsic growth rate, and � is the carrying capacity of
the local environment. The first term is a population growth model and the second term
represents the effects of bird predation, which becomes significant when the population reaches a
critical size �_ and has a maximum value of �. Solve for �at time � = 50 days for � = 0.55 per
day, � 0 = 1000, � = 10), �_ = 10), and � = 10) per day. Use ode45(). Note: you must
make your anonymous function a function of both � and � even though � doesn’t appear
explicitly in the differential equation.