The suspension system of a car uses a spring-mass system to absorb impacts and
dampers to control spring motions. Suppose the spring follows
the Hooke's law of elasticity:
Felastic = -kx:
Let's x k = 25 throughout this problem. Also x the mass m = 1.
Question: Introduce a damper in the suspension to add a drag force that is proportional
to the velocity of the mass,
Fdrag = -gamma*(dx/dt)
(gamma is a postive constant and the negative sign above indicates the drag
force always works)
Fix gamma = 6.
Establish a new DE and nd the particular solution with the initial data x(0) = 0
and x'(0)= -20

Question

The suspension system of a car uses a spring-mass system to absorb impacts and
dampers to control spring motions. Suppose the spring follows
the Hooke's law of elasticity:
Felastic = -kx:
Let's x k = 25 throughout this problem. Also x the mass m = 1.
Question: Introduce a damper in the suspension to add a drag force that is proportional
to the velocity of the mass,
Fdrag = -gamma*(dx/dt)
(gamma is a postive constant and the negative sign above indicates the drag
force always works)
Fix gamma = 6.
Establish a new DE and nd the particular solution with the initial data x(0) = 0
and x'(0)= -20