Page 103 - MATLAB an introduction with applications

88 ——— MATLAB: An Introduction with Applications

P1.22: Consider the given symbolic expressions defined below:
S1 = ‘2/(x – 5)’; S2 = ‘x ^ 5 + 9 * x – 15’; S3 = ‘(x ^ 3 + 2 * x +9) * (x * x – 5)’;
Perform the following symbolic operations using MATLAB.
2
(a) S1S2/S3 (b) S1/S2S3 (c) S1/(S2) 2 (d) S1S3/S2 (e) (S2) /(S1S3)
P1.23: Solve the following equations using symbolic mathematics:
2
(a) x + 9 = 0
2
(b) x + 5x – 8 = 0
3
2
(c) x + 11x – 7 x + 8 = 0
2
3
4
(d) x + 11x + 7x – 19x + 28 = 0
4
3
5
7
(e) x – 8x + 7x + 5x – 8x + 9 = 0
P1.24: Determine the values of x, y and z for the following set of linear algebraic equations:
2x + y – 3z = 11
4x – 2y + 3z = 8
–2x + 2y – z = –6
P1.25: Figure P1.25 shows a scale with two springs.
k k
b
k k
x a

W

Fig. P1.25
The two springs are unstretched initially and will stretch when a mass is attached to the ring and the ring will
displace downwards a distance of x. The weight W of the object is given by
2k
W = ( 0 )(b ) x

where = initial length of a spring = a b 2
2
0
2
and = the stretched length of the spring = a (b ) x 2 .
If k = spring constant,

Write a MATLAB program to determine the distance x when W = 350 N. Given a = 0.16 m, b = 0.045 m,
and the spring constant k = 3000 N/m.
P1.26: Determine the solutions of the following first-order ordinary differential equations using MATLAB’s
symbolic mathematics.
2
(a) y′ = 8x + 5 with initial condition y(2) = 0.5.

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