Answer to Question #175924 in Mechanical Engineering for luke

Question

A spring has a stiffness of 100N/m. A mass of 3 kg was attached to the spring. The mass was pushed 10cm upward from the equilibrium position and was released from rest. Determine the frequency of vibration in Hz.

Answer 1

$k_1=100N/m$

$k_2= \frac{F}{ \delta}= \frac{3 \times9.81}{10 \times 10^{-2}}=294.3 N/m$

The frequency of vibration is given by the formulae below

$f= \frac{1}{2 \pi} \sqrt{ \frac{k_2}{m}}$

Where k is the stiffness of the spring and m is the mass.

$f=\frac{1}{2 \pi} \sqrt{ \frac{294.3}{10 \times10^{-2}}}$

$f=8.634 Hz$