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Out of the following functions, representing motion of a particle, which represents SHM?

1. y = sin ωt − cos ωt
2. y = sin³ ωt
3. y = 5 cos (3π/4 − 3ωt)
4. y = 1 + ωt + ω²t²

Correct answer: y = 5 cos (3π/4 − 3ωt)

Solution

The function y = 5 cos (3π/4 − 3ωt) represents SHM because it is of the standard form y = A cos(ωt + φ), where A is the amplitude, ω is the angular frequency, and φ is the phase constant. The other options do not satisfy this form.

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