Aim :- Compute the first three normal modes and normal mode frequency of N mass ,N+1 spring system fixed at end points .plot the normal modes show that-Wn=nW1.

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Apparatus:- laptop with installed scilab.

Algorithm-
1.input all the values of k,m,N etc.

2.define the zero matrix ‘a’ of order (n,n).
3.use the for-loop (i=2:N-1)
4.define matrix A and end-up the loop
5.write the equation for b=(k/m)a , where ‘a’ is
the matrix defined above.
6.Using the ‘spec’ command find the eigen value
and eigen vector of b.
7.Display the eigen value as frequency.
8.Plot the graph for normal modes and graph
between N and amplitude.

Input:-
1. clf
2. clc
3. k=2
4. m=0.02
5. N=100
6. r=1:N
7. a=zeros(N,N)
8. a(1,[1:2])=[2,-1]
9. a(N,[N-1,N])=[-1,2]
10. for j=2:N-1
11. a(j,[j-1:j+1])=[-1,2,-1]
12. end
13. b=(k/m)*(a)
14. [X,Y]=spec(b)
15. for i=1:3
16. disp(sqrt(Y(i,i)),"frequency(Hz)=")
17. subplot(2,2,i)
18. plot(r',X(:,i))
19. xlabel("N")
20. ylabel("amplitude")
21. title(""+string(i)+"normal mode")
22. end

output:-
frequency(Hz)=
0.3110362
frequency(Hz)=
0.6219972
frequency(Hz)=

0.9328078