SPRING 2016 MATH 152 LAB ASSIGNMENT #3
DUE: MAR., 23
1. Chapter #4
2.The monthly saving P that has to be deposit in a saving account that pays an annual
interest rate of r in order to save a total amount of F in N years can be calculated by
the formula:
F (r/12)
P =
(1 + r/12)12N − 1
Calculate the monthly saving that has to be deposit in order to save $100,000 in 5, 6,
7, 8, 9, and 10 years if the annual interest rate is 4.35%. Display the results in a twocolumn table where the first column is the number of years and the second column is the
monthly deposit.
4.The volume V and the surface area S of a torus shaped water
tube are given by:
1
V = π 2 (r1 + r2 )(r2 − r1 ) and S = π 2 (r22 − r12 )
4
If r1 = 0.7r2 , determine V and S for r2 = 12, 16, 20, 24, and 28 in.
Display the results in a four-column table whrer the first column is
r2 , the second r1 , the third V , and the fourth S.
5. A beam with a length L is attached to the wall with a cable as
shown. A load W = 500 lb is attached to the
√ beam. The tension
W L h2 + x2
force, T , in the cable is given by: T =
hx
For a beam with L = 120 in and h = 50 in., calculate T for x = 10, 30, 50, 70, 90, and 110 in.
13. A round billboard with radius R = 55 in. is
designed to have a rectangular picture placed inside a rectangle with sides a and b. The margins
between the rectangle and the picture are 10 in. at
the top and bottom and 4 in. at each side. Write a
MATLAB program that determines the dimensions
a and b such that the overall area of the picture
1
2
DUE: MAR., 23
will be as large as possible. In the program define
a vector a with values ranging from 5 to 100 with
increments of 0.25. Use this vector for calculating
the corresponding values of b and the overall area of the picture. Then use MATLABs
built-in function max to find the dimensions of the largest rectangle.
25. The surface of many airfoils can be described with an equation of
the form:
p
tc
y = ∓ 0.2
[a0 x/c + a1 (x/c) + a2 (x/c)2 + a3 (x/c)3 + a4 (x/c)4 ]
where t is the maximum thickness as a fraction of the chord length c
(e.g.,tmax = ct). Given that c = 1 m and t = 0.2 m , the following
values for y have been measured for a particular airfoil:
Determine the constants a0 , a1 , a2 ,a3 and a4 . (Write a system of five equations and five
unknowns, and use MATLAB to solve the equations.)
2. Chapter #5
6. Use the fplot command to plot the function f (x) = (sin2x + cos2 5x)e−0.2x in the
domain −6 ≤ x ≤ 6.
10. Two parametric equations are given by:
x = cos3 (t), y = sin3 (t)
u = sin(t), v = cos(t)
SPRING 2016 MATH 152 LAB ASSIGNMENT #3
In one figure, make plots of y versus x and v versus u for 0 ≤ t ≤ 2π . Format the plot
such that the both axes will range from −2 to 2.
x2 − 5x − 12
in the domain −1 ≤ x ≤ 7. Notice that the
x2 − x − 6
function has a vertical asymptote at x = 3. Plot the function by creating two vectors
for the domain of x. The first vector (name it x1) includes elements from −1 to 2.9, and
the second vector (name it x2) includes elements from 3.1 to 7. For each x vector create
a y vector (name themy1 and y2) with the corresponding values of y according to the
function. To plot the function make two curves in the same plot (y1 vs. x1, and y2 vs.
x2). Format the plot such that the y-axis ranges from −20 to 20.
11. Plot the function f (x) =
27. A resistor, R = 4Ω, and an inductor, L = 1.3H, are connected in a circuit to a
voltage source as shown in Figure (a) (an RL circuit). When the voltage source applies
a rectangular voltage pulse with an amplitude of V = 12V and a duration of 0.5s, as
shown in Figure (b), the current i(t) in the circuit as a function of time is given by:
V
i(t) = (1 − e(−Rt)/L ) for 0 ≤ t ≤ 0.5s
R
V (0.5R)/L
−(Rt)/L
i(t) = e
(e
− 1) for 0.5 ≤ ts
R
Make a plot of the current as a function of time for 0 ≤ t ≤ 2s.
35. When monochromatic light passes through a narrow slit it produces on a screen a diffraction pattern consisting of bright and dark
fringes. The intensity of the bright fringes, I, as a function θ of can be
calculated by
sinα 2
πa
I = Imax (
) , where α =
sinθ
α
λ
where λ is the light wave length and a is the width of the slit. Plot the
relative intensity I/Imax as a function of θ for −20◦ ≤ θ ≤ 20◦ .Make
one plot that contains three graphs for the cases a = 10λ ,a = 5λ , and
a = λ. Label the axes, and display a legend.
3