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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written 6.9 years ago by

rakeshrameshpoojari • 80

modified 3.0 years ago by

sagarkolekar ★ 11k

mechanical vibrations

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1 Answer

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written 3.0 years ago by

Krishna_Agrawal • 2.7k

• modified 3.0 years ago

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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