Physics · Simple harmonic motion (S.H.M.) and its equation, phase
Three simple harmonic motions in the same direction having the same amplitude an
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 \( 45^{0}, \) then
- A. the resulting amplitude is \( (1+\sqrt{3}) A \)
- B. the resulting motion is not simple harmonic
- C. The energy associated with the resulting motion \( (3+ \) \( 2 \sqrt{2} \) ) times the energy associated with any single motion
- D. The phase of the resultant motion relative to the first is \( 90^{\circ} \)
Step-by-step solution
The three SHMs have the same amplitude A and frequency, with phases 0°, 45°, and 90°. Using phasor addition, the resultant amplitude is (1+√2)A, so the energy is proportional to (1+√2)^2 = 3+2√2 times the energy of a single motion. The resultant motion is simple harmonic with amplitude (1+√2)A and phase 45° relative to the first.
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