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Applying NLM along 3 Axis

A mass of 2...

Question

A mass of $240 g$ oscillate on a horizontal frictionaless surface at a $f = 3 H z$ and with $a = 4.5 c m$ . what is the effective spring constant for this motion?

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Solution

$k = m g / A$ would be the correct equation to use if the spring was vertical.
Given, $M a s s = 240 g = 0.24 k g,$ $f = 3 H z$ $A = 4.5 c m$
We know that,
$ω = 2 π f = 2 π (3 H z) = 18.8 r a d / s$
Using $w = \sqrt{\frac{k}{m}}$
$\Rightarrow 18.8 r a d / s = \sqrt{(\frac{k}{0.24 k g})} \Rightarrow k = 84.8 N / m$

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