(Solved): 1. While visiting the Chicago museum of Science and Industry, you notice the large simple pendulum ...

1. While visiting the Chicago museum of Science and Industry, you notice the large simple pendulum swings back and forth once every \( \mathrm{T}=7.77 \) seconds. a. Calculate the frequency of oscillation (in Hertz) of the pendulum. (1) b. Calculate the angular frequency \( \omega \) of the pendulum in radians/second. (1) c. Determine the length \( \mathrm{L} \) in meters of the pendulum. (3) d. That evening, your friend told you that the length of the pendulum is actually \( 15 \mathrm{~m} \) and its period is \( 0.02 \) seconds slower than what you have measured. Determine the acceleration due to gravity in \( \mathrm{m} / \mathrm{s}^{2} \) at the museum. (3) e. Would the frequency of this \( 20 \mathrm{~m} \) pendulum be more, less or stay the same if you take this exact pendulum on the moon where gravitational acceleration is much less \( \mathrm{g}_{\text {moon }}=1.625 \mathrm{~m} / \mathrm{s}^{2} \). Calculate and comment. (2)