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Question

Big Ben’s pendulum takes 4s to swing back and forth. The formula t = 2The formula The formula t=2π√(L/32) gives the swing time, t, in seconds, based on the length of the pendulum, L, in feet. What is the minimum length necessary to build a clock with a pendulum that takes longer than
Big ben’s pendulum to swing back and forth?

hintHint:

Substitute the value of t and then find.

The correct answer is: 128 over pi squared


    Complete step by step solution:
    Here we have the formula to be t equals 2 pi square root of L over 32 end root
    Big ben’s pendulum takes 4s, not stretchy rightwards double arrow 4 equals 2 pi square root of L over 32 end root
    On squaring, we have 4 squared equals open parentheses 2 pi square root of L over 32 end root close parentheses squared

    not stretchy rightwards double arrow 16 equals 4 pi squared cross times L over 32
    not stretchy rightwards double arrow pi squared L equals 128
    not stretchy rightwards double arrow L equals 128 over pi squared
    So Big ben's pendulum is 128 over pi squared long. So the minimum length necessary to build a
    clock with a pendulum that takes longer than Big ben’s pendulum to swing back and
    forth is greater than 128 over pi squared.

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