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A particle executes Simple Harmonic Motion in the xy -plane along a straight line given by the equation y = 3 x . The mean position of the particle is at the origin, and the total amplitude of its motion is A₀ . What are the amplitudes of the SHM components along the x -axis and y -axis respectively?

Options

  1. A3 A₀ 2 and A₀ 2
  2. BA₀ 2 and 3 A₀ 2
  3. CA₀ 2 and A₀ 2
  4. DA₀ 3 and 2A₀ 3

Correct answer

B. A₀ 2 and 3 A₀ 2

Step-by-step solution

The path of the particle is a straight line given by y = 3 x . Comparing this with the general equation of a straight line passing through the origin y = ( )x , we get = 3 . This means the line makes an angle = 60^ with the positive x -axis. The total amplitude A₀ is directed along this straight line path. The component of the amplitude along the x -axis is: A_x = A₀ 60^ = A₀ ( 1 2 ) = A₀ 2 The component of the amplitude along the y -axis is: A_y = A₀ 60^ = A₀ ( 3 2 ) = 3 A₀ 2 Thus, the amplitudes along the x -axis

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