Question

8.19 The displacement of a structure is defined by the following equation for a damped oscillation: -kr where k 0.7 and ω 4. (a) Use the graphical method to make an initial estimate of the time required for the displacement to decrease to 3.5. (b) Use the Newton-Raphson method to determine the root to By 0.01%. (c) Use the secant method to determine the root to ε,-0.01%.

Answer 1

ANS::

as for given data

a)

cos 4t 0.27, 3.5 y = 3.5 10

b)

% Newton Raphson Method
 clear all
 close all
 clc
 % Change here for different functions
 f=@(x) 9e^(-.7t)cos(4t)
 %this is the derivative of the above function
 df=@(x) e^(-.7t)*(-36sin(4t)-6.3*(cos(4t)))
 % Change lower limit 'a' and upper limit 'b'
 a=0; b=1;
 x=a;
 for i= .01
 x1=x-(f(x)/df(x));
 x=x1;
 end
 sol=x;
 fprintf('Approximate Root is %.15f',sol)
 a=0;b=1;
 x=a;
 er(5)=0;
 for i=1:1:5
 x1=x-(f(x)/df(x));
 x=x1;
 er(i)=x1-sol;
 end
 plot(er)
 xlabel('Number of iterations')
 ylabel('Error')
 title('Error Vs. Number of iterations')

c)

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