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A simple pendulum consists of a brass sphere of mass m=1kg suspended on a string of length L=1 meter. The pendulum oscillates with an amplitude of 1cm and period of 2 seconds.

What length will a pendulum with a period of 3.683 have?

User Blfuentes
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1 Answer

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The period of a simple pendulum is given by the formula:

T = 2π √(L/g)

where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity (9.81 m/s²).

We can use this formula to solve for the length of the new pendulum:

T = 3.683 s
g = 9.81 m/s²

3.683 = 2π √(L/9.81)

Squaring both sides, we get:

(3.683/2π)² = L/9.81

Solving for L, we get:

L = (3.683/2π)² × 9.81
L ≈ 1.561 meters

Therefore, the length of the new pendulum with a period of 3.683 s is approximately 1.561 meters.
User Azarias
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