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The velocity v of a particle executing simple harmonic motion is given by the equation v = 50 (5 t) cm/s . The amplitude and time period of the motion are, respectively

Options

  1. A50 cm , 0.4 s
  2. B10 cm , 2.5 s
  3. C10 cm , 0.4 s
  4. D50 cm , 2.5 s

Correct answer

C. 10 cm , 0.4 s

Step-by-step solution

The standard equation for the velocity of a particle in simple harmonic motion is: v = A ( t) Given equation: v = 50 (5 t) cm/s Comparing the given equation with the standard equation, we get: = 5 rad/s A = 50 cm/s The time period T is: T = 2 = 2 5 = 0.4 s The amplitude A is: A = 50 = 50 5 = 10 cm Thus, the amplitude is 10 cm and the time period is 0.4 s . Answer: 10 cm , 0.4 s

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