Simple harmonic motion is a type of periodic motion in which an object moves back and forth around a central equilibrium point, with a constant frequency and amplitude. It can be described mathematically using sinusoidal functions.
When a person jumps onto a diving board, the board bends downward due to the person's weight. This bending creates a restoring force that pulls the board back up to its original position. As the board moves up and down, it follows a sinusoidal pattern, exhibiting simple harmonic motion.
The mass of the person on the diving board does not affect the frequency or period of the simple harmonic motion. However, it does affect the amplitude of the motion. A heavier person will cause a greater amount of bending in the board, resulting in a larger amplitude of motion.
The frequency of the simple harmonic motion of a diving board can be affected by the stiffness of the board, the mass of the person on the board, and the strength of the restoring force (determined by the material and design of the board).
Yes, simple harmonic motion can be used to indirectly measure the stiffness of a diving board. The frequency of the motion is directly proportional to the stiffness of the board, so by measuring the frequency and knowing the mass of the person on the board, the stiffness can be calculated using the equation f = 1/(2π)√(k/m), where f is frequency, k is stiffness, and m is mass.