Three simple harmonic motions in the same direction having the same amplitude a and same period are superposed. If each differs in phase from the next by 45o, then:(i) the resultant amplitude is (1+2)a(ii) the phase of the resultant motion relative to the first is 900(iii) the energy associated with the resulting motion is 3+22 times the energy associated with any single motion(iv) the resulting motion is not simple harmonic
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a
(i, iii)
b
(i, ii)
c
(i, iv)
d
(iii, iv)
answer is A.
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Detailed Solution
Resultant y=y1+y2+y3 y=a sin ωt-45o+a sin ωt+a sinωt+45o ⇒ y=1+2a sin ωt So the phase of the resulting motion relative to the first (1) is 45°. As Energy ∝(Amplitude)2 So ERES=1+2aa2=3+22