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Math Help - Differentiation Problem

  1. #1
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    Differentiation Problem

    1. If the equation of motion of a particle is given by s = B cos(ωt + δ), the particle is said to undergo simple harmonic motion. Find the velocity.

    Answer: v(t) = -Bwsin(wt + δ)

    2. When is the velocity = 0?

    Can you please show me step-by-step how to find when the velocity = 0? Thanks.
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  2. #2
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    You need to solve v(t) = -B \omega sin( \omega t + \delta) = 0 for t.

    Since you assume the particle is moving in harmonic motion, having B=0 or  \omega = 0 would contradict that -- so you can safely assume that B, \omega \neq 0. Now all you have to solve is sin( \omega t + \delta) = 0
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  3. #3
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    Quote Originally Posted by Maziana View Post
    1. If the equation of motion of a particle is given by s = B cos(ωt + δ), the particle is said to undergo simple harmonic motion. Find the velocity.

    Answer: v(t) = -Bwsin(wt + δ)

    2. When is the velocity = 0?

    Can you please show me step-by-step how to find when the velocity = 0? Thanks.
    The velocity is equal to zero when
    \sin(\omega t+\delta)=0

    \omega t +\delta =\sin^{-1}(0)

    t=\frac{\sin^{-1}(0) -\delta}{\omega}
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