hw_basicelements

Homework for Garcia 1.2, basic elements of MATLAB

Contents

• Problem 1
• Problem 2
• Problem 3
• Problem 4
• Problem 5
• Problem 6

Problem 1

Consider the equation f = (1/2π)√(k₁k₂/m(k₁+k₂)) where k₁ = 50, k₂ = 100, and m = 2.

• First, assign values for k₁, k₂, and m.
• Next, assign the value to a new variable f, using the variables defined in the first step.

Problem 2

The temperature distribution between to concentric tubes and in the radial direction is:

T = T_b + [(T_a - T_b)ln(b/r)]/ln(b/a)

where r is the radius, and a ≤ r ≤ b. Given T_a = 0, T_b = 100, a = 1, and b = 2:

• Determine the temperature for r = 1.00, 1.01, 1.02, …, 1.99,2.00.
• Plot radial position (r) versus temperature (T) as a solid line.
• On top of that plot, plot every 10th temperature value as a circle.
• Label the axes and provide a title for the plot.

Problem 3

Create two vectors, a row vector whose elements are 2n+1 and a column vector whose elements are 3n+2, for n = 0,1,…,6.

Problem 4

Create a 5x5 square matrix whose elements are -1 along the diagonal and 1 everywhere else. Please define the matrix using any of the following built-in functions: zeros, ones, and diag.

Problem 5

Given the following system of equations

1a + 2b + 3c + 4d = 30

2a + 1b + 3c + 4d = 29

3a + 1b + 2c + 4d = 27

4a + 1b + 2c + 3d = 24

determine a, b, c, and d.

Problem 6

The motion of a particular damped oscillator is described mathematically as the product of a decay function G₁(t) and a sinusoidal function G₂(t):

F(t) = G₁(t)G₂(t) = exp(-t/2)sin(5t)

Reproduce the graph below depicting the decay function G₁(t) and the damped oscillatory motion F(t).

Published with MATLAB® R2014b