The formula t= 2pi sqrt(l/32) relates the time, t, in seconds for a pendulum with the length, l, in feet, to make one full swing back and forth. what is the length of a pendulum that makes one full swing in 2.2 seconds? use 3.14 for pi.

Remark

I like to work from the original equation.

Givens

T = 2.2 seconds

pi = 3.14

L = ??

Substitute and Solve

T = 2*pi*sqrt(L/32) Find the value of 2*pi

2.2 = 2*3.14* sqrt(L/32)

2.2 = 6.28 * sqrt(L/32) Divide both sides by 6.28

2.2/6.28 = sqrt(L/32)

0.35032 = sqrt(L/32) Square both sides.

0.122723 = L/32 Multiply both sides by 32

0.122723 * 32 = L

L = 3.927 feet. <<<<< Length pendulum creating 2.2 seconds.

The length of a pendulum that makes one full swing in 2.2 seconds is 392.71 feet

Given the formula for calculating the length of the pendulum expressed as:

where:

L is the length of the pendulum

T is the period of the pendulum

Given the following parameters:

Period T = 2.2 seconds

Substitute the given parameters into the formula will give;

This shows that the length of a pendulum that makes one full swing in 2.2 seconds is 392.71 feet

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the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!