The period of a pendulum is the time the pendulum takes to swing back and forth. The function L=0.81t^2 relates the length L in feet of a pendulum to the time t in seconds that it takes to swing back and forth. A convention center has a pendulum that is 80 feet long. Find the period.
I am super duper confused! Can someone please explain what in the world I am supposed to do?
I can't find anything anywhere to help me.
T = 2 pi sqrt (L/g)
if you do physics
I will look at your problem in a second
80 = .81 T^2
T^2 = 98.76
T = 9.94 seconds
Now to check that with physics
g is about 32 ft/s^2
T = 2 pi sqrt (80/32)
T = 9.9346 seconds, close enough
Thank you soooo much Damon!
You are welcome.
Of course! I'll explain how to find the period of a pendulum using the given function.
The function L=0.81t^2 relates the length L of the pendulum in feet to the time t in seconds it takes to swing back and forth. We are given that the length of the pendulum is 80 feet.
To find the period, we need to recall a formula for the period of a pendulum. The period T is the time it takes for one complete swing of the pendulum. It can be calculated using the formula:
T = 2π * √(L/g)
Where L is the length of the pendulum and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Since the given function relates L to t, we need to find a way to substitute the given length of the pendulum, 80 feet, into the formula. Here's how we can do it step by step:
Step 1: Convert the length of the pendulum to the same unit used in the formula. Since the formula uses the metric system, we'll convert 80 feet to meters. 1 foot is approximately 0.3048 meters, so:
Length (in meters) = 80 feet * 0.3048 meters per foot
Step 2: Substitute the length into the formula:
T = 2π * √(80 meters / 9.8 m/s^2)
Step 3: Simplify the equation:
T = 2π * √(8.16 / 9.8)
T = 2π * √(0.833)
Step 4: Calculate the square root:
T ≈ 2π * 0.912
Step 5: Multiply by 2π and round the answer to an appropriate decimal place:
T ≈ 5.73 seconds (rounded to two decimal places)
Therefore, the period of the pendulum, with a length of 80 feet, is approximately 5.73 seconds.