coefficient. Let's also assume that ?(0) and ?′(0) are the location and speed of the object
Consider a mass spring system with an external force ?(?) = ?0sin?0?. Let's assume ? is the
mass of the object attached to the spring, ? is the spring constant, and ? is the damping
coefficient. Let's also assume that ?(0) and ?′(0) are the location and speed of the object
attached to the spring at time ? = 0.
a) Find the general solution of the differential equation governing the motion of the spring, in
terms of ?,?,?,?(0),?"(0),?0, and ?o. Your solution shall cover all possible cases
including
1. the case with no damping and ?! is not equal to natural frequency of the system, ? =
sqrt?/?.
2. the case with no damping and ?! is equal to natural frequency of the system, ? =
sqrt?/?.
3. the three cases with damping (overdamped, critically damped, and underdamped).
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