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The oscillation of a body on a smooth horizontal surface is represented by the equation, X = A cos(ωt), where X = displacement at time t, ω = frequency of oscillation. Which one of the following graphs shows correctly the variation of 'a' with 't'?

1. Graph (a)
2. Graph (b)
3. Graph (c)
4. Graph (d)

Correct answer: Graph (b)

Solution

The acceleration 'a' in simple harmonic motion is given by a = -ω²X. Since X = A cos(ωt), a = -ω²A cos(ωt). This means the acceleration is also a cosine function but inverted. Graph (b) correctly represents this relationship.

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