2. Starting from rest, a block of mass m falls through a height h onto a platform with negligible mass, supported by a damped spring. Because of the weight of the mass, the platform will eventually settle down to a new equilibrium position a distance Ar below its original position. (a) To achieve a given value of A.r, what spring constant is required? Determine the damping coefficient required to make this a critically damped system. Think carefully about the initial conditions and then solve for, and sketch the motion of the platform after the mass lands on it. What is the minimum height, h, that will cause the platform to temporarily overshoot (fall below) its final equilibrium position? (b) With the same spring constant as in part (a), let us increase the damping coefficient so that the system becomes overdamped. With the same initial conditions as in part (a), solve for the motion of the platform after the mass lands on it, and note that the damping coefficient, B, is an arbitrary parameter in this solution. For what value of 8 will the platform most quickly settle down to its new equilibrium position, without overshoot?set t= 0 do instant block reaches plot form XIDj= AX , V(0)= - Egh Let LID V=1Jagh KAY= MS K= AX - Wa = K B=J2 xity= (An +Act) e BE X ID)= AX = AN X(t) = LAxe-# + Ante."#t ) X()= -Baxe"#* + ALe" - BAzte At Kit)= [- Bax + As - BAit]e BE * [D) = - Jagh = - BAX +AZ AL= - Bah + BAX *() = (-Bax - Jagh + BAX - B(- Jagr + BAX) t) e-At * (t) = ( -Jagh + BJagh - BRAX t ) e-BE =) xIt) = lax+ [-Jagh + BAX)t) e- BE XIt)= ( AX - Jagh + + Jgaxtje" Jet The System overshoots If X(t)