Question

A 2.0-kg block oscillates with a frequency of 14.5 Hz at the end of a certain spring. The spring is then cut into two halves. The 2.0-kg block is then made to oscillate at the end of one of the halves. What is the frequency of oscillation of the block?

Answer 1

When the spring is cut in half and the 2.0-kg block is made to oscillate at the end of one of the halves, the frequency of oscillation remains the same.

Step-by-step explanation:

In this scenario, the 2.0-kg block is made to oscillate at the end of one of the halves of the spring. When the spring is cut in half, the effective spring constant of each half is double the original spring constant. However, the frequency of oscillation of a mass-spring system only depends on the spring constant and the mass, and is given by the formula:

f = 1/(2π) * √(k/m)

Since the mass remains the same, the frequency of oscillation will still be 14.5 Hz, regardless of whether it is oscillating with the entire spring or one of the halves.