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A small object of mass 1 kg is attached to a spring with spring constant 2N/m. This
Chapter 2, Problem 4(choose chapter or problem)
A small object of mass 1 kg is attached to a spring with spring constant 2N/m. This spring-mass system is immersed in a viscous medium with damping constant 3 N.s/m. At time t = 0, the mass is lowered 1/2 m below its equilibrium position, and released. Show that the mass will creep back to its equilibrium position as t approaches infinity
Questions & Answers
QUESTION:
A small object of mass 1 kg is attached to a spring with spring constant 2N/m. This spring-mass system is immersed in a viscous medium with damping constant 3 N.s/m. At time t = 0, the mass is lowered 1/2 m below its equilibrium position, and released. Show that the mass will creep back to its equilibrium position as t approaches infinity
ANSWER:Step 1 of 2
Let be the position of the mass away from the equilibrium position at time .
Write the differential equation as follows.
The initial conditions will be and .
Write the charecteristic equation and find roots.
The general solution will be as follows.