The ratio of tfull (time for a full swing) to thalf (time for a half swing) for the given simple pendulum is approximately 2:1.
The ratio of tfull to thalf for a simple pendulum swinging on the surface of the Earth is influenced by the principles of harmonic motion. In a simple pendulum, the time period of oscillation (T) is directly proportional to the square root of the length of the pendulum (L) and inversely proportional to the square root of the acceleration due to gravity (g). Mathematically, this relationship is represented as T = 2π√(L/g).
When comparing the time for a full swing (tfull) to the time for a half swing (thalf), we can observe that the length of the pendulum remains constant in both cases. Therefore, the primary factor affecting the ratio is the acceleration due to gravity. As the pendulum moves from the equilibrium position (4) to the extreme position (-4) during a full swing, the effect of gravity on the pendulum's motion is more pronounced, leading to a longer time period compared to the time it takes to move from 2 to -2 during a half swing. Consequently, the ratio tfull/thalf is approximately 2:1, reflecting the characteristic behavior of a simple pendulum in harmonic motion.