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A.1 Spring Oscillators a. A mass m is attached via a spring with spring constant k to a wall, with the mass allowed to move along a horizontal surface. The surface provides a resistive force proportional to the velocity Ex = -2myr. Using N2, write down a differential equation describing the displacement of the mass from its equilibrium position, e(t), then determine the solution for e(t) in the most general form possible by assuming a trial solution 2 = e b. Rewrite the solution from part (a) in amplitude-phase form (you don't need to derive this, just state it). Under the assumption that is very small so you can ignore additive terms of order y or higher, prove that the total energy in the system goes down with time as E (5) e(t) = zkaže-21 .- [5]