Final answer:
The motion of a pendulum can be described as a simple harmonic motion. At the center of oscillation, the pendulum is at its highest potential energy point and zero kinetic energy. Unfortunately, without knowing the mass of the pendulum bob, we cannot calculate the energy accurately.
Step-by-step explanation:
The motion of a pendulum can be described as a simple harmonic motion. A pendulum oscillates back and forth around a fixed point called the equilibrium position. The time it takes for one complete oscillation is called the period. The motion of the pendulum can be represented by the equation T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
In this case, the pendulum has a length of 15 centimeters. Since the equation for the period depends on the length of the pendulum, we can use it to calculate the period of this pendulum. However, the question specifically asks about the energy of the pendulum at the center of oscillation, so we need to focus on that.
At the center of oscillation, the pendulum is at its highest potential energy point and zero kinetic energy. This is because the pendulum is momentarily stationary before changing its direction of motion. As the pendulum moves away from the center, it loses potential energy and gains kinetic energy.
At the endpoints of the oscillation, the pendulum is at its lowest potential energy point and maximum kinetic energy.To calculate the energy at the center of oscillation, we need to know the mass of the pendulum bob and the speed at which it crosses the point of equilibrium.
Unfortunately, the given information does not include the mass of the bob. Without knowing the mass, we cannot calculate the energy accurately. Therefore, we cannot determine the energy of the pendulum at the center of oscillation with the given information.