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December 20, 2014

December 20, 2014

Posted by **Elisa** on Wednesday, August 6, 2008 at 12:12am.

Would I have to calculate the force of the pulley and the object in order to do this problem? How would I do it?

- physics -
**drwls**, Wednesday, August 6, 2008 at 4:06amFor the fundamental frequency to change by an octave, the tension T in the string must vary by a factor of 4. (Wave speed and fundamental frequency vary with the square root of the tension).

Consider how large an amplitude the pendulum must swing to have the tension vary by a factor of four. The largest tension will occur at the bottom of the swing, when the speed and centripetal force are highest. The least tension will occur at the maximum swing angle, A.

Maximum tension:

Tmax = M g + M Vmax^2/L

(1/2)Vmax^2 = g L(1 - cos A)

Tmax = M g [1 + 2 (1 - cosA)]

= M g [3 - 2 cos A]

Minimum tension occurs at maximum angle A, when there is no centripetal acceleration, and is

Tmin = M g cos A

Setting Tmax/Tmin = 4 will let you finish the problem and solve for the angle A.

Check my thinking. I may have made a math error along the way.

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