I am not able to solve value of 3 constants with three equations

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Sahir Jan
Sahir Jan on 3 Nov 2021
Answered: Bjorn Gustavsson on 3 Nov 2021
c1*(cos(b*d)+cosh(b*d))+c3*(sin(b*d)+sinh(b*d))+c4*(sin(b*d)-sinh(b*d))=0
c1*(cos(b*(L-d))+cosh(b*(L-d)))+c3*(sin(b*(L-d))+sinh(b*(L-d)))+c4*(sin(b*(L-d))-sinh(b*(L-d)))=0
c1*(-cos(b*L)+cosh(b*L))+c3*(-sin(b*L)+sinh(b*L))+c4*(-sin(b*L)-sinh(b*L))=0
I have the following three equations and have to find the value for c1, c3 and c4. Can someone help me with the code
Thank you

Answers (1)

Bjorn Gustavsson
Bjorn Gustavsson on 3 Nov 2021
For given values of b, d, and L you have a standard system of linear equation. An obvious solution to these equations are all ci = 0. Each equation will be an equation for a plane in the three-dimensional space for c1, c2, c4. From there you can use geometric arguments that either 2 planes are parallel and doesn't intersect or intersects along a line, in the second case such a line either intersects the third plane, lies in the third plane or does not intersect the plane, the third case is out since we know that [0 0 0] is a solution, therefor either [0 0 0] is the only solution or lies on the line. What you'll have to do is to check whether there is a line of solutions or the one and only solution.
HTH

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