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(a) Split up the harmonic x = 8 sin(ωt + 45°), into two harmonic motions, one of which has amplitude of 10 and phase difference zero.
(a) A body is subjected to two harmonic motion as x1= 15 sin(ωt+30°) and x2= 8 cos(ωt + 60°). What extra motion could be given to the body to bring it equilibrium?
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(Hint Minimization problem -min X1 + X2, s.t. 2X1 + X2 = 12, X1 + 6X2 = 24, 5X1 + 8X2 = 24; X1, X2 = 0).
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