Question

What is the period of a pendulum consisting of a \(6.0-\mathrm{kg}\) mass oscillating on a 4.0 -m-long string?

Short answer

Answer: The period of the pendulum is approximately 4.03 s.

Step-by-step solution

Identify the given values and the formula to use

We are given the mass of the pendulum (\(6.0\, \mathrm{kg}\)) and the length of the string (\(4.0\, \mathrm{m}\)). We need to find the period (T) of the pendulum. The formula to use is: \(T = 2\pi\sqrt{\frac{\mathrm{L}}{\mathrm{g}}}\).

Plug in the given values

Now, substitute the given values into the formula: \(T = 2\pi\sqrt{\frac{4.0\, \mathrm{m}}{9.81\, \mathrm{m/s^2}}}\).

Calculate the period

Calculate the square root of the ratio and then multiply by \(2\pi\): \(T \approx 2\pi\sqrt{0.408} \approx 4.03\, \mathrm{s}\).

Write the answer

The period of the pendulum with a \(6.0\, \mathrm{kg}\) mass oscillating on a \(4.0\, \mathrm{m}\)-long string is approximately \(4.03\, \mathrm{s}\).