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# LaPlace Transforms and Differential Equations : Masses and Springs

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In system below spring k1 is anchored at the left side and has a spring constant of k1, spring K2 has a spring constant of k2; the system is not subjected to friction or damping.

Block M is subjected to a periodic driving force f(t) = A sin(&#969;t).

Both masses are initially at rest in the equilibrium position

Using Laplace transforms, derive and solve the initial value problem for the displacement function.

Show that if m and K2 are chosen so that &#969;= (K2/m)^1/2 that m cancels the forced vibration of M.

See attached file for full problem description.

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LaPlace Transforms and Differential Equations are applied to Masses and Springs.The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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