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MMLU-Pro / 9864 / A particle executing simple harmonic motion given by y = 4 sin (2…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

A particle executing simple harmonic motion given by y = 4 sin {(2\pit / 6) + \alpha} is displaced +1 unit when t = 0. Find: (a) the phase angle when t = 0; (b) the difference in phase between any two positions of the particle 2 seconds apart? (c) the phase angle corresponding to a displacement of +2; (d) the time necessary to reach a displacement of +3 from the initial position.

category

physics

options

  1. Phase angle at t = 0: π/6 radians, Phase difference between two positions 2 seconds apart: 240 degrees, Phase angle corresponding to a displacement of +2: 60 degrees, Time to reach a displacement of +3: 0.38 seconds
  2. Phase angle at t = 0: π/2 radians, Phase difference between two positions 2 seconds apart: 150 degrees, Phase angle corresponding to a displacement of +2: 37.5 degrees, Time to reach a displacement of +3: 0.63 seconds
  3. Phase angle at t = 0: π/8 radians, Phase difference between two positions 2 seconds apart: 45 degrees, Phase angle corresponding to a displacement of +2: 11.25 degrees, Time to reach a displacement of +3: 1.52 seconds
  4. Phase angle at t = 0: π/6 radians, Phase difference between two positions 2 seconds apart: 60 degrees, Phase angle corresponding to a displacement of +2: 15 degrees, Time to reach a displacement of +3: 1.14 seconds
  5. Phase angle at t = 0: π/12.4 radians, Phase difference between two positions 2 seconds apart: 60 degrees, Phase angle corresponding to a displacement of +2: 15 degrees, Time to reach a displacement of +3: 1.14 seconds
  6. Phase angle at t = 0: π/10 radians, Phase difference between two positions 2 seconds apart: 300 degrees, Phase angle corresponding to a displacement of +2: 75 degrees, Time to reach a displacement of +3: 0.19 seconds
  7. Phase angle at t = 0: π/3 radians, Phase difference between two positions 2 seconds apart: 90 degrees, Phase angle corresponding to a displacement of +2: 45 degrees, Time to reach a displacement of +3: 0.76 seconds
  8. Phase angle at t = 0: π/12.4 radians, Phase difference between two positions 2 seconds apart: 120 degrees, Phase angle corresponding to a displacement of +2: 30 degrees, Time to reach a displacement of +3: 0.57 seconds
  9. Phase angle at t = 0: π/24.8 radians, Phase difference between two positions 2 seconds apart: 240 degrees, Phase angle corresponding to a displacement of +2: 60 degrees, Time to reach a displacement of +3: 0.28 seconds
  10. Phase angle at t = 0: π/4 radians, Phase difference between two positions 2 seconds apart: 180 degrees, Phase angle corresponding to a displacement of +2: 22.5 degrees, Time to reach a displacement of +3: 0.95 seconds

src

stemez-Optics

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Source and history

upstream_id / Original problem ID
9864
task_id
88b52bfd-6962-5d88-a221-09a9cf2f0dae
task_key
default--test--9864
task_revision_id
1
config / split
default / test

Official source

initial import