For the mass on the spring, how is the period of the harmonic motion related to the spring constant, k?

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For the mass on the spring, how is the period of the harmonic motion related to the spring constant, k?

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Answer 1 · 2018-03-17T09:49:24

Suppose a mass of $m$ $m$ is attached to a spring of spring constant $K$ $K$ is lying on a horizontal floor,then you pull the mass such that the spring got stretched by $x$ $x$ ,so restoring force acting on the mass due to the spring is $F = - K x$ $F=-Kx$

We can compare this with equation of S.H.M i.e $F = - m ω^{2} x$ $F=-momega^2x$

So,we get, $K = m ω^{2}$ $K=m omega^2$

So, $ω = \sqrt{\frac{K}{m}}$ $omega =sqrt(K/m)$

Hence time period is $T = \frac{2 π}{ω} = 2 π \sqrt{\frac{m}{K}}$ $T=(2pi)/omega =2pi sqrt(m/K)$

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For the mass on the spring, how is the period of the harmonic motion related to the spring constant, k?

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