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A pendulum set up in the stairwell of a tall building consists of a steel ball of mass 208 kg suspended at the end of a 24.0 m wire. What is the period of oscillation?

Answer :

Final answer:

The period of oscillation for a pendulum with a 24.0 m wire and a 208 kg steel ball is approximately 9.82 seconds, using the standard formula T = 2π√(l/g) for a simple pendulum.

Explanation:

To find the period of oscillation for a pendulum, we can use the formula for the period of a simple pendulum, which is T = 2π√(l/g), where T is the period, l is the length of the pendulum, and g is the acceleration due to gravity, assuming small angles of oscillation. For a pendulum with a 24.0 m wire, assuming the acceleration due to gravity (g) is the standard 9.81 m/s2, the period T is calculated as follows:

First, substitute the values into the formula: T = 2π√(24.0 m / 9.81 m/s2).

Calculate the square root: √(24.0 m / 9.81 m/s2) = √(2.447) ≈ 1.564 s.

Then multiply by 2π: T ≈ 2 * 3.14159 * 1.564 s ≈ 9.82 s.

Therefore, the period of oscillation of the pendulum is approximately 9.82 seconds.

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