Final answer:
The length of the pendulum rod, given a period of 20 seconds for small-amplitude oscillations, is approximately 99.29 meters. This calculation assumes the value of gravity is 9.81 m/s^2.
Step-by-step explanation:
The student is asking about the length of the rod in a simple pendulum given that the period of oscillation is 20 seconds. The simple pendulum can be studied in Physics to understand simple harmonic motion (SHM). The formula for the period T of a simple pendulum is T = 2π√(L/g), where L is the length of the rod and g is the acceleration due to gravity. We can rearrange this formula to solve for L as follows:
L = (T/(2π))2 × g
Substituting the period T = 20 seconds and using the standard acceleration due to gravity g = 9.81 m/s2, we can calculate the length of the rod. After computing, we find that the length of the rod is approximately 99.29 meters. It’s important to note that this calculation assumes the oscillation amplitude is small, which is typically less than 15°.