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We are given the mass $m$, amplitude $A$, and period $T$ of a body undergoing Simple Harmonic Motion. Newton's Second Law tells us that


so that $F$ is maximum when $x$ is maximum, that is, when we have $x=A$. Thus,


since we have a spring system. We can obtain $\omega$ from $T$ by

\begin{displaymath}\omega=2\pi f=\frac{2\pi}{T}.\end{displaymath}

This yeilds a value for $k$ of

\begin{displaymath}k=(2\pi f)^2m=118\;\textrm{N/m},\end{displaymath}

and a value of the maximum force of $10\;{\textrm N}$.

Dan Cross 2006-10-18