A spring with spring constant 8 Newtons per meter is attached to the ceiling. A

Question

A spring with spring constant 8 Newtons per meter is attached to the ceiling. A 2 kg mass is attached. The system is set in motion in a medium that imparts a damping force numerically equal to 8 times the velocity. The mass is started from the equilibrium position and released with a downward velocity of 4 cm per second. Find the equation of motion. Is this system over damped, critically damped , or under damped? An external force f(t)= 12sin(t) Newtons is applied to the system in the previous problem. Find the new equation of motion using the Method of Undetermined Coefficients.

Explanation / Answer

new equation of motion will be solution of d2x/dt2=4x 6sint-9.8 x= c1e^2t +c2e^-2t - 1.25sint + 2.45

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