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NTA Abhyas JEE Main2020PhysicsOscillationsPractice

A particle executes simple harmonic motion and it is located at x = a , b and c at time t 0 , 2 t 0 a n d 3 t 0 respectively. The frequency of the oscillation is:

Options

  1. A1 2 π t 0 cos - 1 ⁡ a + c 2 b
  2. B1 2 π t 0 cos - 1 ⁡ a + 2 b 3 c
  3. C1 2 π t 0 cos - 1 ⁡ a + b 2 c
  4. D1 2 π t 0 cos - 1 ⁡ 2 a + 3 c b

Correct answer

A. 1 2 π t 0 cos - 1 ⁡ a + c 2 b

Step-by-step solution

a = A sin ⁡ ω t 0 b = A sin ⁡ 2 ω t 0 c = A sin ⁡ 3 ω t 0 a + c = A sin ⁡ ω t 0 + sin ⁡ 3 ω t 0 = 2 A sin ⁡ 2 ω t 0 cos ⁡ ω t 0 ∵ sin C + sin D = 2 sin C + D 2 cos C − D 2 ω = 1 t 0 cos - 1 ⁡ a + c 2 b ⇒ f = 1 2 π t 0 cos - 1 ⁡ a + c 2 b

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