Problem 3 Background will vibrate when it is set into motion. It The natural fre

Question

Problem 3 Background will vibrate when it is set into motion. It The natural frequency, wn, is the frequency at which a system is a value that mechanical, civil and aerospace engineers compute when examining structures. Problem Statement You are a civil engineer and want to find the natural frequency of a structure you are designing. In order to determine this frequency it is necessary to use the quadratic equation to solve for the roots of: Ax2 Bx C A 3 100 B 1.15 x 104 C 2.7 x 10 where: Hint: Use the quadratic formula. The MATLAB command sqrt can be used to take the square root of a value or you can take the (1/2) power of the value. The two solutions, x, to the quadratic equation are real and positive. To determine the two natural frequencies, con take the square root of the x values. The units of on will be in rad/s. Print the answer to the screen in the format shown below using an fprintf statement. Make sure to include the correct number of decimal places. The natural frequencies are X.xx rad/s and x.xx rad/s.

Explanation / Answer

%matlab code

a = 100;
b = -1.15*10^4;
c = 2.7*10^5;

% calculating determinant
d = (b*b)-(4*a*c);

% calculate x1
x1 = (-b + sqrt(d))/(2*a);

% calculating x2
x2 = (-b - sqrt(d))/(2*a);

w1 = sqrt(x1);
w2 = sqrt(x2);

% displaying the output to 2 decimal places
fprintf('The natural frequencies are %0.2f rad/s and %0.2f rad/s ',w1,w2);

%output:
% The natural frequencies are 9.06 rad/s and 5.73 rad/s

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