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# Answer to Question #182161 in Mechanical Engineering for luke

Question #182161

A spring has a stiffness of 100N/m. A mass of 4 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

1
Expert's answer
2021-04-21T07:05:45-0400

"k_1=100N\/m"

"k_2= \\frac{F}{ \\delta}= \\frac{4 \\times9.81}{10 \\times 10^{-2}}=392.4 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{392.4}{10 \\times10^{-2}}}"

"f=9.9698 Hz"

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