Don M.

asked • 08/26/21# Pendulum Problem

Directions: Complete the following problem showing as much work as possible.

You are considering installing a pendulum in the amusement park visitor’s center. The time it takes a pendulum to complete a full cycle or swing depends upon the length of the pendulum. The formula is given by T = 2 π √(L/32) where T represents the time in seconds and L represents the length of the pendulum in feet.

If the pendulum is 8 feet long, how long will it take for the pendulum to complete a full cycle? (10 points)

You’d like your pendulum to take 20 seconds to complete a cycle. How long will the pendulum need to be? Is this reasonable in your building, which is planned to be 20 feet high? (10 points)

---PLEASE GIVE EXACT ANSWERS PLEASE---

## 2 Answers By Expert Tutors

T = 2 π √(8)/(32) = 2 π √(1/4) = 2 π (1/2) = π ∼ 3.14159... seconds

Solving for L:

T = 2 π √(L/32)

Solving for L:

T = ( (2 π) / √(32) ) √(L) = ( (2 π) / 4 √(2) ) √(L) = ( π / (2 √(2)) ) √(L)

√(L) = T / ( π / (2 √(2)) ) = (2 √2 ) T / π

squaring both sides:

L = 8 T^{2} / π^{2} or 8 (T/π)^{2}

for T = 20 seconds:

L = 8 (20/π)^{2} = 324.2 feet which is obviously much greater than 20 feet

Yefim S. answered • 08/26/21

Math Tutor with Experience

T = 2π√L/32 = 2π√8/32 = π s = 3.14 s

L = 32T^{2}/(4π^{2}) = 32·20^{2}/(4π^{2}) = 324.23 ft > 20 ft. Not reasonable

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Mark M.

Veiify that this is not part of a test/quiz/exam. Getting and giving assistance on such is unethical.08/26/21