Question

A 100-coil spring has a spring constant of 540 N/m. It is cut into four shorter springs, each of which has 25 coils. One end of a 25-coil spring is attached to a wall. An object of mass 76 kg is attached to the other end of the spring, and the system is set into horizontal oscillation. What is the angular frequency of the motion? Number Entry field with incorrect answer now contains modified data Units Entry field with correct answer

Answer 1

Answer:

w = 5.3311 rad/sec

Explanation:

n = 100 has a k = 540 N/m

k depends on the number of coils by:

$k = \frac{G*d^4}{8*n*D^3}$

By the design equation we see that the spring stiffness k has an inverse relationship with number of coils n.

Hence, when n = 25 coils ; k = 4* 540 = 2160 N/m

The relationship between angular frequency and k is:

$w = \sqrt{\frac{k}{m} }\\\\Hence,\\\\w = \sqrt{\frac{2160}{76} }\\\\w = 5.3311 rad/sec$