# Question: consider an underdamped 1d oscillator of mass m and spring...

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Consider an underdamped 1D oscillator of mass m and spring constant k that is subjected to a damping force of F~ drag = −b ˙~x. (Assume that the mass is on a horizontal frictionless table so you only need to consider the spring force and the drag force). At time t = 0 the system is released from rest at x = A. (a) What is the solution for x(t)? Take the derivative to find ˙x(t). (b) Use part (a) to find an expression for the total energy E(t). (Hint: use trig rules to simplify) (c) Find the rate of energy loss, dE/dt, and show that it is proportional to ˙x^2 . (d) Is the rate of energy loss a constant? Are the any times when the energy loss rate is 0? Explain why this makes sense.