Question

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 45° , then

(a) the resultant amplitude is (1 + √2)a

(b) the phase of the resultant motion relative to the first is 90°

(c) the energy associated with the resulting motion is (3 + 2√2) times the energy associated with any single motion

(d) the resulting motion is not simple harmonic 

Answer 1

Correct option  (a) and (c) 

Explanation:

The resultant of the given three simple harmonic motions is 

The resultant is also a simple harmonic motion with amplitude A equals to a(√2 +1)

The energy associated with the resultant motion is 1/2mA²ω²

The energy associated with any single motion is 1/22ma²ω²