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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 th e resulting motion is (3 + 2√2) times the energy associated with any single motion
  • d)
    the resulting motion is not simple harmonic.
Correct answer is option 'A,C'. Can you explain this answer?
Verified Answer
Three simple harmonic motions in the same direction having the same am...
From superposition principle
y = y1 + y2 + y3
= a sin ωt + a sin (ωt + 45°)  + a sin (ωt + 90°)
= a[sin ωt + sin (ωt + 90°] + a sin (ωt + 45°)
= 2a sin (ωt + 45°) cos 45° + a sin (ωt + 45°)
= (√2 +1) a sin (ωt + 45°)
= A sin (ωt + 45°)
Therefore resultant motion is simple harmonic of amplitude A = (√2 +1) a
and which differ in phase by 45° relative to the first.
Energy in SHM ∝ (amplitude)2
 
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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)ab)the phase of the resultant motion relative to the first is 90°c)the energy associated with th e resulting motion is (3 + 2√2) times the energy associated with any single motiond)the resulting motion is not simple harmonic.Correct answer is option 'A,C'. Can you explain this answer?
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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)ab)the phase of the resultant motion relative to the first is 90°c)the energy associated with th e resulting motion is (3 + 2√2) times the energy associated with any single motiond)the resulting motion is not simple harmonic.Correct answer is option 'A,C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 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)ab)the phase of the resultant motion relative to the first is 90°c)the energy associated with th e resulting motion is (3 + 2√2) times the energy associated with any single motiond)the resulting motion is not simple harmonic.Correct answer is option 'A,C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)ab)the phase of the resultant motion relative to the first is 90°c)the energy associated with th e resulting motion is (3 + 2√2) times the energy associated with any single motiond)the resulting motion is not simple harmonic.Correct answer is option 'A,C'. Can you explain this answer?.
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