Physics · Simple harmonic motion (S.H.M.) and its equation, phase
A body of mass is in S.H.M and its displacement is given by the relation \mathrm
A body of mass \( 1 / 4 \mathrm{kg} \) is in S.H.M and its displacement is given by the relation \( \boldsymbol{y}=\mathbf{0 . 0 5 \operatorname { s i n }}\left(\mathbf{2 0 t}+\frac{\boldsymbol{\pi}}{\mathbf{2}}\right) \mathrm{m} . \) If \( \boldsymbol{t} \) is in seconds, the maximum force acting on the particle is:
- A. 5 N
- B. 2.5 N
- C. 10 N
- D. 0.25 N
Step-by-step solution
From the displacement equation y = 0.05 sin(20t + π/2), amplitude A = 0.05 m, angular frequency ω = 20 rad/s. Maximum acceleration a_max = ω²A = (20)² × 0.05 = 400 × 0.05 = 20 m/s². Mass m = 1/4 kg = 0.25 kg. Maximum force F_max = m a_max = 0.25 × 20 = 5 N.
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