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14_P64InstructorSolution - 14.64 Model Assume the...

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14.64. Model: Assume the small-angle approximation. Visualize: Solve: The tension in the two strings pulls downward at angle . θ Thus Newton’s second law is 2 sin y y F T ma θ = − = From the geometry of the figure we can see that 2 2 sin y L y θ = + If the oscillation is small, then y L ± and we can approximate sin / . y L θ Since y / L is tan , θ this approximation is equivalent to the small-angle approximation sin tan θ θ if 1 rad. θ ± With this
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