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please as soon as posiible Problem 1: A mass-spring system, that satisfies the conditions y

`(0)=0.16`

and

`y^(')(0)=0.0`

, is described by a homogenous second-order linear ODE with constant coefficients as follows:

`m(d^(2)y)/(dx^(2))+b(dy)/(dx)+ky=0`

Given that

`m=10,k=90,b`

may take two values 100 or 10 . For each case, find: The particular solution. Hint: use the initial conditions to solve for the unknown coefficients. Determine which case is: overdamped, critically damped, or underdamped. If possible, compute the damping ratio (

`\zeta `

), the natural frequency (wn), and the damped frequency ( wd ).