Answer to Question #175923 in Mechanical Engineering for luke

Question

A spring extends 2 inches when loaded vertically with 4 lbs. This weight was pulled further down by 3 inches an was released from rest. Determine the frequency of vibration in rad per second

Answer 1

$k = f/x$

where; k is the spring constant.

f is the force applied.

x is the extension on the spring.

4lbs = 1.81 kgs

2inches = 0.0508 m

3inches = 0.0762 m

k= 18.1Newtons/ 0.0508m

= 356.3 N/m

force required to extend the spring to a further 3inches (0.0762m)

$f = kx$

= 356.3 N/m *0.0762

= 27.15N

$W (Rads/sec) = \sqrt {k/m}$

$= \sqrt {356.3/2.715 }$

= 11.455 rads/sec