n-coupled oscillator-- both series, and parallel. Hi all. Ok, the title is a bit deceptive, as that is typically used to denote a string type oscillator system. In this case, I'm referring to multiple masses, and multiple springs. To be specific, we're doing a system with 5 masses, and 13 springs. This means that there are 2 to 4 springs connected either in parallel, or in series to each of the masses. From what I remember-- parallel springs are treated as: 1/k_eff = 1/k1 + 1/k2+ ... + 1/kn. Where n is the nth spring, and k is the spring constant. And series springs are just k_eff = k1 + k2 + ... + kn. (the sum of all spring constants.) Did I get this backwards, or is it correct? Next, because we're doing a 5 mass system, we'll have a 5 x 5 matrix for the M matrix. Where the masses will be the diagonal elements of the M matrix. The K matrix however will be more complicated. Which is why I'm here. It seems to me-- from previous lectures, and homework problems-- that the only elements of the K matrix that will have any non-zero values will be the diagonal, and the elements one space to the left, and one space to the right of the diagonal elements. Is this correct? E.g. for a 2 x 2 matrix, the elements would be k_11 -k_12 -k_21 k_22 In this case, the k_12 element = k_21. The reason would be due to a non-restoring force acting ON x_2, etc... If we then expand this matrix out to n x n-- anything larger than a 2 x 2, all other elements--- e.g. sample 3 x 3 mat. k_11 -k_12 0 -k_21 k_22 -k_23 0 -k_32 k_33 As you can see, only the diagonal, and "immediate" off-diagonal elements are non-zero. My question-- does this play out in ALL oscillator matrices? I have asked my prof., but he has yet to answer. In my specific 5 x 5 K matrix, this would in fact give me 13 elements, accounting for the 13 springs of the system. The general equation to solve this system would be: M^-1 K A = omega^2 A where M, and K are n x n matrices, A is a column vector (and can be used to obtain our eigenvectors/normal modes), and omega^2 is the eigenvalue to the system-- can be multiple eignevalues. A clarification of this aspect of a multiple oscillator system would be deeply appreciated. Thanks.