A 1.0-kg block oscillates with a frequency of 10 Hz at the end of a certain spring. The spring is then cut into two halves. The 1.0-kg block is then made to oscillate at the end of one of the halves. What is the frequency of oscillation of the block?
A)5 Hz
B)10 Hz
C)14 Hz
D)20 Hz
E)40 Hz

Question

Quizplus · Accepted Answer

When the spring is cut into two halves, each half will have half of the original spring constant. This means the new spring will have a higher frequency of oscillation, according to the equation f = (1/2π) √(k / m). Since the mass of the block hasn't changed, the new frequency of oscillation will be f = (1/2π) √(2k / m). Substituting in k = 2k/2 and m = 1 kg, we get f = (1/2π) √(2(2k) / 1) = √2 / π times the original frequency. Therefore, the new frequency will be 14.14 Hz, or approximately 14 Hz. The correct answer is (C).

A 10-Kg Block Oscillates with a Frequency of 10 Hz at at the End