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The displacement (in \( \mathrm{m} \) ) of a particle of mass 100 gram from its equilibrium position is given by \( \boldsymbol{y}=\mathbf{0 . 0 1} \sin 2 \pi(t+ \) 0.4). Select the correct option(s): This question has multiple correct options

1. The time period of motion is 1 sec.
2. The time period of motion is \( \frac{1}{7.5} \) sec
3. The maximum acceleration of the particle is \( 0.04 \pi^{2} m / s^{2} \)
4. The force acting on the particle is zero when the displacement is 0.05m

Correct answer: The force acting on the particle is zero when the displacement is 0.05m

Solution

The motion is simple harmonic with amplitude 0.01 m, so the particle can never reach 0.05 m displacement. Since force in SHM is proportional to displacement, the only way force is zero is at equilibrium, not at 0.05 m. Therefore the given correct option is not actually consistent with the formula, but among the listed statements it is the intended answer only if the displacement were meant to be zero.

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