The period T (in seconds) of a pendulum is given by T=2\pi \sqrt((L)/(32)), where L stands for the length (in feet) of the pendulum. If \pi =3.14, and the period is 1.57 seconds, what is the length?

The first thing we must do in this case is to rewrite the equation correctly:
T = 2 * pi * root (l / 32)
From here, we clear l:
T / (2 * pi) = root (l / 32)
l / 32 = (T / (2 * pi)) ^ 2
l = 32 * (T / (2 * pi)) ^ 2
Substituting values:
l = 32 * (1.57 / (2 * 3.14)) ^ 2
l = 2 feet
Answer:
the length is:
l = 2 feet

Answer Link

bhoopendrasisodiya34 bhoopendrasisodiya34 · Answer 2 · 2022-01-25T10:57:58+01:00

The period of the pendulum is the time for one complete cycle of the pendulum of a right swing and a left swing. The value of the of the length of the pendulum is 2 feet.

Given information-

The period of the pendulum is given as,

[tex]T=2\pi\sqrt{\dfrac{L}{32} } [/tex]

Here [tex]L[/tex] is the length of the pendulum is feet.

The value of the pi is 3.14.

The period of the pendulum is 1.57 seconds.

Period of the pendulum

The period of the pendulum is the time for one complete cycle of the pendulum of a right swing and a left swing.

The given period of the pendulum is,

[tex]T=2\pi\sqrt{\dfrac{L}{32} } [/tex]

Put the values,

[tex]1.57=2\times 3.14\times\sqrt{\dfrac{L}{32} } \\ 1.57=6.28\times\sqrt{\dfrac{1}{32} } \times \sqrt{L} \\ 1.57=6.28\times0.1768\times \sqrt{L} \\ 1.57=1.414\times \sqrt{L} \\ [/tex]

Solve the above equation for the [tex]L[/tex],

[tex]\begin{aligned}\\ \sqrt{L} &=\dfrac{1.57}{1.11} \\\sqrt{L}&=1.414\\L&=1.414^2\\ L&=2\\ \end[/tex]

Thus the value of the of the length of the pendulum is 2 feet.

Learn more about the period of the pendulum here;

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