1. (40‘) The suspension system of a car uses a spring-mass system to absorb impacts anddampers (or shock absorbers) to control spring motions. Suppose the spring followsthe Hooke‘s law of elasticity which means the displacement of the mass is in directproportion with the load added to itFelastic -kx:Let‘s x k 25 throughout this problem. Also x the mass m 1.(1i) (7‘) Introduce a damper in the suspension to add a drag force that is proportionalto the velocity of the mass,Fdrag -gamma*(dx/dt)Here, is a postive constant and the negative sign above indicates the dragforce always works against the motion of the mass submerged in it. Fix gamma 6.Establish a new DE and nd the particular solution with the initial data x(0) 0and x‘(0) -20
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