Question

A mass of 22 kg is suspended from a spring with a spring constant of 11

N/m and then released, creating periodic motion. At what distance below the
natural length of the spring will the mass finally come to rest? (Recall that g =
9.8 m/s²)

Answer 1

The mass will finally come to rest at a distance of 0 meters below the natural length of the spring.

Step-by-step explanation:

In this question, we have a mass of 22 kg suspended from a spring with a spring constant of 11 N/m. When the mass is released, it undergoes periodic motion. To find the distance below the natural length of the spring where the mass finally comes to rest, we can use the equation for the potential energy of the spring-mass system:

PE = (1/2) k x^2,

where PE is the potential energy, k is the spring constant, and x is the displacement from the natural length of the spring. At rest, the potential energy is at its minimum (zero), so we can set the equation equal to zero and solve for x:

(1/2) k x^2 = 0,

k x^2 = 0,

x^2 = 0.

Since (x^2) = 0,

x = 0.

The mass will finally come to rest at a distance of 0 meters below the natural length of the spring.