Math

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 t=0).

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  1. Make a situation diagram where you have a triangle with the vertical angle as Ø, the hypotenuse 50 cm (the pendulum) and a vertical leg of 49 cm
    so we would get
    cosØ - 49/50 = .98
    then Ø = .20033.. (I stored that in my calculator to keep accuracy)

    so we have
    (1/4)sin(πt/2) = .20033..
    sin (πt/2) = .801339...
    πt/2 = .9295...
    t = .5917577 or π - .59175.. = 2.5498...

    the pendulum will be 1 cm above its rest position at
    t = appr .59 seconds or at t = appr 2.55 seconds

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  2. my first equation should have been

    cosØ = 49/50 = .98

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  3. The second answer is wrong it should be 3.41seconds instead of 2.55s

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