Consider a linear array of n masses, each equal to m, connected by n + 1 springs, all massless and having spring constant k, with the outer ends of the first and last springs fixed. The masses can move without friction in the linear dimension of the array.
a) Write the equations of motion for the masses.
b) Configurations of motion for which all parts of a system oscillate with the same angular frequency are called normal modes of the system; the corresponding angular frequencies are the system's normal-mode angular frequencies. Find the normal-mode angular frequencies of this array.
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