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A coin is placed on a horizontal platform, which undergoes vertical simple harmonic motion of angular frequency ω. The amplitude of oscillations is gradually increased. The coin will have contact with the platform for the first time. (i) at the higher position of the platform (ii) at the mean position of the patform (iii) for an amplitude of g/ω2 (iv) for an amplitude of √2/ω
  • a)
    Only (i) is correct
  • b)
    (i) and (iv) are correct
  • c)
    (i),(ii) and (iii) are correct
  • d)
    Only (iii) is correct
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A coin is placed on a horizontal platform, which undergoes vertical si...
Ω. The amplitude of the motion is A.

At any given time t, the platform is at a vertical displacement y from its equilibrium position. The displacement of the coin from this position is x, which can be expressed as:

x = A cos(ωt)

where cos(ωt) represents the position of the platform relative to its equilibrium position at time t.

The acceleration of the platform at time t is given by:

a = -ω^2y

This means that the acceleration of the coin at time t is:

a = -ω^2(y + x)

Substituting x, we get:

a = -ω^2(y + A cos(ωt))

The force acting on the coin is given by:

F = ma = -mω^2(y + A cos(ωt))

where m is the mass of the coin.

Thus, the force acting on the coin is proportional to its displacement from the equilibrium position, and varies sinusoidally with time. This is consistent with the behavior of a harmonic oscillator.
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A coin is placed on a horizontal platform, which undergoes vertical simple harmonic motion of angular frequency ω. The amplitude of oscillations is gradually increased. The coin will have contact with the platform for the first time. (i) at the higher position of the platform (ii) at the mean position of the patform (iii) for an amplitude of g/ω2 (iv) for an amplitude of √2/ωa)Only (i) is correctb)(i) and (iv) are correctc)(i),(ii) and (iii) are correctd)Only (iii) is correctCorrect answer is option 'D'. Can you explain this answer?
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