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The time T, in seconds, it takes a pendulum to make one swing depends on the length of the pendulum and is given byT(L) = 2 L32where L is the length of the pendulum in feet.(a) Find the time (in seconds) it takes the pendulum to make one swing if the length of the pendulum is 6 ft. Round to the nearest hundredth of a second.________ sec(b) Find the time it takes (in seconds) the pendulum to make one swing if the length of the pendulum is 9 in. Round to the nearest tenth of a second.________ sec

Respuesta :

The expression of the time taken to swing the pendulum is,

[tex]T(L)=2\pi\sqrt[]{\frac{L}{32}}[/tex]

Part (a)

Substitute the known values in the expression of time.

[tex]\begin{gathered} T(L)=2(3.14)\sqrt[]{\frac{6}{32}} \\ =(6.28)(0.433) \\ \approx2.72\text{ s} \end{gathered}[/tex]

Thus, the time taken by pendulum to complete one swing is 2.72 s.

Part (b)

Convert the length of pendulum in feet as,

[tex]\begin{gathered} 9\text{ in=}(9\text{ in)(}\frac{1\text{ ft}}{12\text{ in}})_{} \\ =0.75\text{ ft} \end{gathered}[/tex]

Substitute the known values in the expression of time.

[tex]\begin{gathered} T(L)=2(3.14)\sqrt[]{\frac{0.75}{32}} \\ =(6.28)(0.153) \\ \approx1.0\text{ s} \end{gathered}[/tex]

Thus, the time taken by pendulum to complete one swing is 1.0 s.

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