SOLUTION: The formula T = 2π√(l/g) relates a pendulum's period, T, in seconds (the time it takes to swing back and forth) to its length, l, in centimeters using g, the gravitation

Algebra ->  Radicals -> SOLUTION: The formula T = 2π√(l/g) relates a pendulum's period, T, in seconds (the time it takes to swing back and forth) to its length, l, in centimeters using g, the gravitation      Log On


   

Question 1026264: The formula T = 2π√(l/g) relates a pendulum's period, T, in seconds (the time it takes to swing back and forth) to its length, l, in centimeters using g, the gravitational acceleration of 981 cm/sec^2.
How long would the pendulum have to be (to the nearest tenth of a centimeter) to make a pendulum with the given period?
QUESTION:
Solve the equation T = 2π√(l/g) for l
NOTE:
√(l/g) means square root of l/g
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the formula is T+=+2+%2A+pi+%2A+sqrt%28L%2Fg%29.

i use capital L because it's less easy to be confused with the number one.

what you need to do is solve this equation for L.

the given period is T.

start with T+=+2+%2A+pi+%2A+sqrt%28L%2Fg%29.

divide both sides of this equation by (2 * pi) to get:

T+%2F+%282+%2A+pi%29+=+sqrt%28L%2Fg%29.

square both sides of this equation to get:

%28T%2F%282%2Api%29%29%5E2+=+L%2Fg.

multiply both sides of this equation to get:

g%2A%28T%2F%282%2Api%29%29%5E2+=+L

that's your answer.

L+=+g%2A%28T%2F%282pi%29%29%5E2

for example, if the given period is 5 seconds, then the formula would becomes:

5+=+2+%2A+pi+%2A+sqrt%28L%2Fg%29.

you would solve for L to get:

L+=+g%2A%285%2F%282pi%29%29%5E2

since g = 981, the formula would become:

L+=+981%2A%285%2F%282pi%29%29%5E2

this results in L = 621.2255072 centimeters.

if you go back to the original formula, then it becomes:

T+=+2+%2A+pi+%2A+sqrt%28621.255072%2F981%29.

that results in T = 5.

any discrepancy will be due to rounding.

i used internally stored numbers and the answer came exactly to 5.

the number of 621.255072 that you see has been rounded to the number of digits that the calculator can display.

using that only will give you an answer that is close to 5, but not right on.