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A series of problems to solve.. eigenvalue equation, I do not understand, in self-study A (n + 1) - 5An + 6A (n-1) = 0 A1 = 1 A2 = 1 to find the general term formula of sequence
a(n+1)-5an+6a(n-1)=0
a(n+1)-2an = 3(an-2a(n-1))
[a(n+1)-2an]/(an-2a(n-1)) =3
[a(n+1)-2an]/(a2-2a1) =3^(n-1)
a(n+1)-2an = -3^(n-1)
an-2a(n-1) =-3^(n-2)
an + (1/3).3^n = 2[ a(n-1) + (1/3).3^(n-1)]
[an + (1/3).3^n]/[ a(n-1) + (1/3).3^(n-1)] =2
[an + (1/3).3^n]/[ a2 + (1/3).3^2] = 2^(n-2)
an + (1/3).3^n = 2^n
an = 2^n-3^(n-1)
If there are multiple roots in the root of the characteristic equation when solving the general term of the sequence, what should we do?
It is equal root, and there are more than two (not quadratic equation, higher than this)
It is not the only solution for some problems
Test: 1, to see if there is a statement is an increasing function or positive or negative
2. The same sign of two odd numbers in the equal ratio sequence
Elastic potential energy formula
How to ask for it
According to Hooke's law, f = KX
And the work is equal to the force times the distance, so the elastic potential energy of displacement x is expressed as the triangle area under the diagonal KX on the F-X diagram
So e = x * KX / 2
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