Consider a system of 3 springs (A, B and C) connected in a line. The left hand end of spring A is anchored to a wall as is the right hand end of spring C. Between springs A and B is mass M and between springs B and C is mass N.
Consider the following 2 situations:
1. mass M = N and the spring constants are spring A = k. B=2k, C=k
2. mass M = 2N and the spring constants are A=4k, B=k, C = k
Find the characteristic frequencies and the characteristic modes of vibration for the 2 situations.