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Math Help - Solving Trigonometry

  1. #1
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    Solving Trigonometry

    1) When a pendulum 0.5m long swings back and forth, its angular displacement Ɵ from rest position, in radians is given by Ɵ=1/4sin((pi/2)t), where t is the time, in seconds. At what time(s) during the first 4 s is the pendulum displaced 1 cm vertically above its rest position? (assume the pendulum is at its rest position at 0).


    I don't understand, the maximum is 0.25. Could someone solve with an explanation of the question?
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  2. #2
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    Re: Solving Trigonometry

    You are correct that the maximum answer to that equation is 0.25. But i think you are incorrect in your assumptions about what that number is. That is an angle. Specifically 1/4th of a radian or about 14.32 degrees.

    Look at this diagram:


    The pendulum swings from point b to point d.

    The forumla
    \Theta=\frac{1}{4} \sin(\frac{\pi}{2} t)
    This gives us:
    \angle bac = \angle edc
    Just remember that these angles are in radians and you should convert them to degrees by multiply by \frac{180}{\pi}

    L = .5m = ab = ad.

    So we need to find an \theta such that ed=.01m (1cm)

     \cos(\theta) = \frac{ed}{cd}

     \cos(\theta) = \frac{.01}{cd}

    \cos(\theta) = \frac{ab}{ad+cd}

    \cos(\theta)=\frac{.5}{.5+cd}

    \frac{.01}{cd} = \frac{.5}{.5+cd}

    I will assume you can take it from here once you figure out cd then solve for theta
    Then plug theta back into the original equation to find t
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