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Consider a situation in which a mass of size M is hanging from a vertical spring with spring constant K. There is a damping component on the spring which has a damping constant of C. (a) Write out a second-order homogenous differential equation to represent this situation. (b) Keeping in mind that M, K, and C are all positive, find the generalized solution of the differential equation in terms of M, K, and C. (Assume that 4MK > C2) (c) What does your solution function represent in the problem's physical context?

Consider a situation in which a mass of size M is hanging from a vertical spring with spring constant K. There is a damping component on the spring which has a damping constant of C. (a) Write out a second-order homogenous differential equation to represent this situation. (b) Keeping in mind that M, K, and C are all positive, find the generalized solution of the differential equation in terms of M, K, and C. (Assume that 4MK > C2) (c) What does your solution function represent in the problem's physical context?

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  1. (4 points) Consider a situation in which a mass of size M is hanging from a vertical spring with spring constant K . There is a damping component on the spring which has a damping constant of C . (a) Write out a second-order homogenous differential equation to represent this situation. (b) Keeping in mind that M , K , and C are all positive, find the generalized solution of the differential equation in terms of M , K , and C. (Assume that 4 M K > C 2 ) (c) What does your solution function represent in the problem's physical context?

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