The mechanics of a mass-spring system is governed by the differential equation m \frac{d^{2} y}{d t^{2}}+l \frac{d y}{d t}+k y=0 ; \quad y(0)=0.5, y^{\prime}(0)=0 \text { where } m=1+a, l=5+\mathrm{b} \text { and } k=6+c \text {. Here } a, b \text { and } c \text { are } 2^{\text {nd }}, 3^{\text {rd }} \text { and } 4^{\text {th }} \text { digits of your } ) Find the solution of the differential equation and describe the behaviour of the-mass )) An external force of f(t) = 5e-3t + sin(2t) is applied to the mass, what effect does it have on the motion of the mass? Find a scenario by choosing appropriate constant values for the spring system-where no dampening occurs. How does this affect the frequency and amplitude of the oscillations?[5]

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