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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

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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(ωt).

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 ω= (K2/m)^1/2 that m cancels the forced vibration of M.