Physics · Simple harmonic motion (S.H.M.) and its equation, phase
A particle executes of amplitude and time period What is the minimum time requir
A particle executes \( \boldsymbol{S} \boldsymbol{H} \boldsymbol{M} \) of amplitude \( 25 c m \) and time period \( 3 s \) What is the minimum time required for the particle to move between two points \( 12.5 \mathrm{cm} \) on either side of the mean position?
- A. \( 0.5 s \)
- B. \( 1.0 s \)
- C. \( 1.5 s \)
- D. 2.0
Step-by-step solution
Angular frequency ω = 2π/T = 2π/3 rad/s. For SHM x = A cos(ωt) with A=25 cm, positions ±12.5 cm (half amplitude) correspond to phases ωt = π/3 and 2π/3. The time difference is (2π/3 - π/3)/ω = (π/3)/(2π/3) = 0.5 s. This is the minimum time to move directly between the two points through the mean position.
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