Physics · Simple harmonic motion (S.H.M.) and its equation, phase
The displacement (in ) of a particle of mass 100 gram from its equilibrium posit
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
- A. The time period of motion is 1 sec.
- B. The time period of motion is \( \frac{1}{7.5} \) sec
- C. The maximum acceleration of the particle is \( 0.04 \pi^{2} m / s^{2} \)
- D. The force acting on the particle is zero when the displacement is 0.05m
Step-by-step solution
From y = 0.01 sin(2π(t+0.4)), ω = 2π rad/s, so time period T = 2π/ω = 1 s. Option C is also correct: maximum acceleration = ω^2 A = (2π)^2 × 0.01 = 0.04π^2 m/s^2. Option D is false because force is zero only at equilibrium (y=0).
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