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NEET2015PhysicsOscillationsActual

When two displacements represented by y 1 = a   s i n ⁡ ( ω t ) and y 2 = b cos ⁡ ω t are superimposed the motion is:

Options

  1. Anot a simple harmonic.
  2. Bsimple harmonic with amplitude a b .
  3. Csimple harmonic with amplitude a 2 + b 2 .
  4. Dsimple harmonic with amplitude a + b 2 .

Correct answer

C. simple harmonic with amplitude a 2 + b 2 .

Step-by-step solution

y 1 = a sin ⁡ ω t y 2 = b cos ⁡ ω t = b sin ⁡ ω t + π 2 Amplitude A = a 2 + b 2 + 2 a b cos ⁡ π 2 A = a 2 + b 2 Since the frequency for both motion are same, then the resultant motion will be SHM.

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