Question

The period T (in seconds) of a pendulum is given by T=2πL32 , where L stands for the length (in feet) of the pendulum. If π=3.14 , and the period is 3.14 seconds, what is the length? T=2pi times the square root of L/32

Answer 1

8 feet

Explanation:

We are given the formula for the period T (in seconds) of a pendulum by:

`T = 2\pi \sqrt{(L)/(32) }` where L stands for the length (in feet) of the pendulum and we are to find its length if the period is 3.14 seconds.

For that, we will square everything to make the square root vanish:

`T^2=4\pi ^2(L)/(32)`

Multiplying both sides by 32 to get:

`4\pi ^2 L = 32 T^2`

Dividing both sides by
`4\pi ^2`:

`L=(32T^2)/(4\pi ^2)`

Now substituting the given value of T to find the length L:

`L= (32(3.14)^2)/(4\pi ^2)`

`L=8`

Therefore, the length of the pendulum is 8 feet.

Answer 2

The length of the pendulum is 8 units

Explanation:

The period T (in seconds) of a pendulum is given by

`T=2\pi \sqrt{(L)/(32) }`.

We want to find the value of
`L`, when
`T=3.14` and
`\pi=3.14`.

We substitute the given values into the formula to get,

`3.14=2(3.14) \sqrt{(L)/(32) }`.

We divide through by 3.14 to get,

`1=2\sqrt{(L)/(32) }`.

We divide both sides by 2, to obtain,

`(1)/(2)=\sqrt{(L)/(32) }`.

We square both sides to get,

`((1)/(2))^2=(L)/(32)`

`(1)/(4)=(L)/(32)`

We now multiply both sides by 32 to get,

`(1)/(4)* 32=(L)/(32)* 32`

We cancel out the common factors to get,

`8=L`

Hence,the length of the pendulum is 8 units