Question
A mass m is placed on a platform from a height 'h'. The platform is attached to a spring whose other end is fixed to the ground. Find the compression in the spring, if the spring constant is k.
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Answer
Drop in potential energy = Energy stored in spring
$\text{mg}(\text{h}+\text{x})=\frac{1}{2}\text{kx}^2$
2 mgh + 2 mgh = kx2
kx2 – 2 mgh – 2 mgh = 0
$\text{x}=\frac{2\text{mg}\pm\sqrt{4\text{m}^2\text{g}^2-4\text{k}.2\text{mgh}}}{2\text{k}}$
$\Rightarrow\text{x}=\frac{\text{mg}}{\text{k}}\pm\frac{\text{mg}}{\text{k}}\sqrt{1-\frac{2\text{kh}}{\text{mg}}}$.
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