Question

Consider a mass hanging vertically from a spring and at equiLiBrium. If you pull it down by 4 cm and release it, it begins to oscillate at a frequency f1. If you had pulled it down instead by 8 cm, what would its frequency of oscillation be? Assume simple harmonic motion.

Answer 1

The frequency of oscillation of a mass hanging from a spring in simple harmonic motion remains constant, regardless of whether it is pulled down by 4 cm or 8 cm, as the frequency is independent of amplitude.

Step-by-step explanation:

In the context of simple harmonic motion (SHM), the frequency of oscillation for a mass-spring system is independent of the amplitude of the oscillations. This means that whether one pulls down the mass by 4 cm or 8 cm, as long as the other conditions like the mass and the spring constant remain unchanged, the frequency of oscillation f1 will remain the same. This is because the frequency f is determined by the formula f = (1/2π) * sqrt(k/m), where k is the spring constant, m is the mass, and sqrt denotes the square root function. Thus, the displacement, or how far the spring is stretched or compressed from its equilibrium position, does not affect the frequency.