The period t ( in seconds) of a simple pendulum as a function of its length l(in feet) is given by t(l) = xpie sqrt 1/32.2
a. Express the length l as a function of the period t
b. How long is a pendulum whose period is 3 seconds.
Is the answer 2 sec for a and 2.25 feet for b?????
Someone please help me with this!!!!
Good luck :D
the length of a simple pendulum varies directly with the square of its period. if a pendulum of length 2.25 meters has a period of 3 seconds, how long is a pendulum of 8 seconds?
To solve this problem, let's start with part a.
a. Express the length l as a function of the period t:
Given the equation:
t(l) = xπ√(1/32.2)
To express the length l as a function of the period t, we need to isolate l on one side of the equation. Start by squaring both sides of the equation to remove the square root:
[t(l)]^2 = (xπ)^2 * (1/32.2)
Simplifying further:
l^2 = (xπ)^2 * (1/32.2)
To isolate l, take the square root of both sides:
l = √[(xπ)^2 * (1/32.2)]
So, the expression for length l as a function of the period t is:
l = xπ * √(1/32.2)
Moving on to part b:
b. How long is a pendulum whose period is 3 seconds.
Given the period t = 3 seconds, we can substitute this value into the expression we obtained in part a:
l = xπ * √(1/32.2)
l = xπ * √(1/32.2) ≈ (2.25 feet)
No, the answer for part b is not 2 seconds. It is approximately 2.25 feet.