Question

Suppose a spring with spring constant 9 N/m is horizontal and has one end attached to a wall and the other end attached to a mass. You want to use the spring to weigh items. You put the spring into motion and find the frequency to be 0.9 Hz (cycles per second). What is the mass? Assume there is no friction.

Answer 1

To find the mass attached to a spring when the frequency of oscillation is known, use the formula for the frequency of SHM (f = (1/2π) ∙ √(k/m)) and rearrange it to solve for mass.

Step-by-step explanation:

To determine the mass attached to a horizontal spring where the frequency of oscillation is known, we can use the formula for the frequency of a mass-spring system undergoing simple harmonic motion (SHM), which is f = (1/2π) ∙ √(k/m), where f is the frequency, k is the spring constant, and m is the mass. Given a spring constant 9 N/m and a frequency 0.9 Hz, we can rearrange the formula to solve for the mass (m = k / (2πf)^2). Plugging in the values, we get the mass m = 9 N/m / (2π ∙ 0.9 Hz)^2, which we can calculate to find the mass of the object attached to the spring.