rn 3) Consider the second order differential equation mx = -kr ba' describing a mass spring

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3) Consider the second order differential equation mx" = -kr – ba' describing a mass spring system with damping. Suppose the mass of the object is m = 1 kg, the spring constant is k = 1/4 and damping constant is b = 1/2.. i) Plug in the guess r(t) = est to both sides of the DE and determine values of s such that r(t) = est is a solution. Note: solutions will involve complex values of s. ii) Expand one of your guesses using Euler's formula and use the real and imaginary parts of this to form the general solution to the DE. iii) Find values for your constants above to describe releasing the mass from rest with initial displacement of 4 (i.e. x(0) = 4, x'(0) = 0). 3) Consider the second order differential equation mx" = -kr – ba' describing a mass spring system with damping. Suppose the mass of the object is m = 1 kg, the spring constant is k = 1/4 and damping constant is b = 1/2.. i) Plug in the guess r(t) = est to both sides of the DE and determine values of s such that r(t) = est is a solution. Note: solutions will involve complex values of s. ii) Expand one of your guesses using Euler's formula and use the real and imaginary parts of this to form the general solution to the DE. iii) Find values for your constants above to describe releasing the mass from rest with initial displacement of 4 (i.e. x(0) = 4, x'(0) = 0).

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