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A vertical spring mass system has mass of 0.5 kg and an Initial deflection of 0.2cm. Find the spring stiffness and natural frequency of the system.
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Given,

m = 0.5 kg

δ = 0.2 cm

According to question,

Spring stiffness = ?

Natural frequency = ?


Spring Stiffness is given by,

$stiffness = (\frac {mg}{δ})$

$stiffness = (\frac {0.5 \times 9.81}{0.2/100})$

$stiffness = 2452.5 N/m$


Frequency is given by,

$F_n = (\frac {1}{2π}) \times (\frac {g}{δ}) $

$F_n = (\frac {1}{2π}) \times (\frac {9.81}{0.2/100\ m}) $

$F_n = 11.14\ Hz\ Ans.$

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