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

# 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 $\left(1+\sqrt{2}\right)\mathrm{a}$(ii) the phase of the resultant motion relative to the first is 900(iii) the energy associated with the resulting motion is $\left(3+2\sqrt{2}\right)$ times the energy associated with any single motion(iv) the resulting motion is not simple harmonic

1. A

(i, iii)

2. B

(i, ii)

3. C

(i, iv)

4. D

(iii, iv)

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### Solution:

Resultant $\mathrm{y}={\mathrm{y}}_{1}+{\mathrm{y}}_{2}+{\mathrm{y}}_{3}$

So the phase of the resulting motion relative to the first (1) is 45°.

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