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Two mutually perpendicular simple harmonic vibrations have same amplitude, frequency and phase. When they superimpose, the resultant form of vibration will be
- a)A circle
- b)An ellipse
- c)A straight line
- d)A parabola
Correct answer is option 'C'. Can you explain this answer?
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Resultant of Mutually Perpendicular Simple Harmonic Vibrations
Explanation:
When two simple harmonic vibrations are perpendicular to each other, they are known as mutually perpendicular simple harmonic vibrations.
Let's consider two simple harmonic vibrations with the same amplitude, frequency, and phase:
- x = A cos (ωt) and y = A cos (ωt + π/2)
When these two vibrations are superimposed, we get the resultant vibration (z) as follows:
- z = √(x² + y²) = A √(cos²(ωt) + cos²(ωt + π/2))
Simplifying the above equation, we get:
- z = A √(cos²(ωt) + sin²(ωt)) = A
Thus, the resultant vibration is a straight line passing through the origin with an amplitude equal to the amplitude of the individual vibrations.
Conclusion:
Hence, when two mutually perpendicular simple harmonic vibrations with the same amplitude, frequency, and phase are superimposed, the resultant vibration is a straight line passing through the origin.
Explanation:
When two simple harmonic vibrations are perpendicular to each other, they are known as mutually perpendicular simple harmonic vibrations.
Let's consider two simple harmonic vibrations with the same amplitude, frequency, and phase:
- x = A cos (ωt) and y = A cos (ωt + π/2)
When these two vibrations are superimposed, we get the resultant vibration (z) as follows:
- z = √(x² + y²) = A √(cos²(ωt) + cos²(ωt + π/2))
Simplifying the above equation, we get:
- z = A √(cos²(ωt) + sin²(ωt)) = A
Thus, the resultant vibration is a straight line passing through the origin with an amplitude equal to the amplitude of the individual vibrations.
Conclusion:
Hence, when two mutually perpendicular simple harmonic vibrations with the same amplitude, frequency, and phase are superimposed, the resultant vibration is a straight line passing through the origin.
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Two mutually perpendicular simple harmonic vibrations have same amplitude, frequency and phase. When they superimpose, the resultant form of vibration will bea)A circleb)An ellipsec)A straight lined)A parabolaCorrect answer is option 'C'. Can you explain this answer?
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