Exam-style question
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If the displacement of an object in simple harmonic motion is given by x(t) = A cos(ωt), where A is the amplitude and ω is the angular frequency, what is the expression for the velocity (v) as a function of time?.
- A.v(t) = -Aω sin(ωt)
- B.v(t) = Aω cos(ωt)
- C.v(t) = -Aω cos(ωt)
- D.v(t) = A sin(ωt)
Model answer
What a good answer should say
- v(t) = -Aω sin(ωt)
Explanation
Why this works
The velocity is derived by differentiating the displacement function with respect to time, resulting in v(t) = -Aω sin(ωt), which shows the relationship between velocity and displacement in SHM.
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