Final answer:
The statement is false; a simple pendulum executes simple harmonic motion during its entire cycle if the amplitude is less than 15 degrees. The length of a pendulum with a period of 1.00 second can be calculated using the formula for a simple pendulum's period.
Step-by-step explanation:
The statement that a simple pendulum is executing simple harmonic motion 41% of the time is False. A simple pendulum continuously undergoes simple harmonic motion (SHM) for small amplitudes (< 15 degrees) during its entire cycle, not just a percentage of the time. In SHM, the restoring force is directly proportional to the displacement from the equilibrium position. The period of a simple pendulum is determined by its length and the acceleration due to gravity, not by the concept of mental energy or psychokinesis.
Regarding the length of a pendulum with a period of 1.00 s, it can be computed using the formula for the period of a simple pendulum T = 2π√(L/g), where L is the length in meters and g is the acceleration due to gravity (9.81 m/s2). Solving for L would give us the desired length. For a lightly damped oscillator, the amplitude decreases by a certain percentage each cycle, but this is a separate concept from the time spent undergoing SHM.