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The displacement of a body undergoing simple harmonic motion is given by the equation y = 12 (4 t - 4 ) cm . The amplitude and time period of the oscillation are respectively

Options

  1. A12 ~cm , 0.5 ~s
  2. B12 ~cm , 2.0 ~s
  3. C12 ~m , 0.5 ~s
  4. D12 ~m , 2.0 ~s

Correct answer

A. 12 ~cm , 0.5 ~s

Step-by-step solution

The standard equation for simple harmonic motion is given by y = A ( t + ) . Comparing the given equation y = 12 (4 t - 4 ) cm with the standard equation, we get: Amplitude A = 12 ~cm Angular frequency = 4 ~rad/s The time period T is given by T = 2 . Substituting the value of , we get: T = 2 4 = 0.5 ~s Therefore, the amplitude is 12 ~cm and the time period is 0.5 ~s . Answer: 12 ~cm , 0.5 ~s

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