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We want to superpose the oscillations of / simple harmonic oscillators having the same frequency w and amplitude A, but differing from one another by constant phase increments of that is E(t) = A cos(wt) + Acos(wt + a) + Acos(wt + 20) + ... + Acos(wt + (N -1)0) (a) Show the following. Hint: you can use the geometric series, or graphical phasor addition. E(t) = A x sin(No/2) N - 1 x cos wt + sin(a/2) 2 (b) Calculate (E'(t)), where (...) denotes time-average. Sketch to scale (E2(t)) as a function of a for N = 2; N = 3; and N = 10. Clearly indicate the maximum and minimum values, and values of o where the extrema occur. This calculation is the basis of finding radiation from antenna arrays, interference of multiple slits (N = 2 is the familiar double slit result) and diffraction gratings