Answer:
w = 5.3311 rad/sec
Explanation:
n = 100 has a k = 540 N/m
k depends on the number of coils by:
[tex]k = \frac{G*d^4}{8*n*D^3}[/tex]
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:
[tex]w = \sqrt{\frac{k}{m} }\\\\Hence,\\\\w = \sqrt{\frac{2160}{76} }\\\\w = 5.3311 rad/sec[/tex]
