Physics · JEE | OSCILLATIONS
हिन्दीGiven below are two statements: Statement I: A combination of two simple harmonic motions with arbitrary amplitudes and frequencies is always periodic. Statement II: A periodic motion can always be expressed as a superposition (sum) of an infinite number of harmonic motions with appropriate amplitudes. In the light of the above statements, choose the most appropriate answer from the options given below:
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Correct answer · Option D
Statement I is incorrect but Statement II is correct.
Explanation
Statement I is incorrect because combination of SHMs is periodic only if their frequencies are commensurable (integral multiples); Statement II is a standard Fourier theorem fact and is correct.