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Q.

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
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