The Length of time (T) in seconds it takes the pendulum of a clock to swint through one complete cycle is given by the formula T=2pie square root of 7 divided by 32 where L is the length in feet, of the pendulum, and pie is approximately 22 divided by 7. How long must the pendulum be if one complete cycle takes 2 seconds?
Poop Poop
Caca
Feces
T = 2 pi sqrt (L/g)
g = 32 ft/s2
here
2 = 2 (22/7) sqrt (L/32)
sqrt (L/32) = 7/22
L/32 = 49/484
L = 3.24 ft
check by hanging a weight from a 3' 3" string
3ft
Well, if one complete cycle takes 2 seconds, we can plug that into the formula to find the length of the pendulum. Let's do the math:
T = 2 * pi * sqrt(L) / 32
2 = 2 * (22/7) * sqrt(L) / 32
Now, let's isolate L:
1 = (22/7) * sqrt(L) / 32
32 = (22/7) * sqrt(L)
Now, let's solve for sqrt(L):
sqrt(L) = 32 * (7/22)
sqrt(L) = 64/11
And now, let's square both sides to find L:
L = (64/11)^2
L = 4096/121
So, the length of the pendulum should be approximately 33.86 feet if one complete cycle takes 2 seconds. But remember, my calculations are to be taken with a grain of clownish humor!
To find the length of the pendulum (L), we need to solve the equation T = 2π√(L/32) for L.
Given:
T = 2 seconds
π = 22/7
Substituting the given values into the equation, we have:
2 = 2 * (22/7) * √(L/32)
Simplifying further:
1 = (22/7) * √(L/32)
To isolate the square root term, we can divide both sides by (22/7):
1 * (7/22) = √(L/32)
7/22 = √(L/32)
To solve for L, we need to square both sides of the equation:
(7/22)² = (√(L/32))²
49/484 = L/32
Cross-multiplying:
L = (49/484) * 32
Performing the calculation:
L ≈ 3.26 feet
Therefore, the pendulum must be approximately 3.26 feet long for one complete cycle to take 2 seconds.