The motion of the mass-spring-dashpot system is described by the solution of the differential y” + 4y' + 13y = 0. equation (a) Find the general solution of the equation.

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Chapter2: Second-order Linear Odes
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The motion of the mass-spring-dashpot system is described by the solution of the differential
equation
y" + 4y' + 13y = 0.
(a) Find the general solution of the equation.
Transcribed Image Text:The motion of the mass-spring-dashpot system is described by the solution of the differential equation y" + 4y' + 13y = 0. (a) Find the general solution of the equation.
(b) Determine whether the motion is underdamped, critically damped or overdamped, and describe
the motion of the spring system.
(c) Find the general solution of the spring system as above assuming that there is no damping force
but the external force F(t) = 4 sin(√13t) is applied to the object from its equilibrium position
with no initial velocity. Describe a possible motion of the spring system. Do not solve for
the unknown constants.
Transcribed Image Text:(b) Determine whether the motion is underdamped, critically damped or overdamped, and describe the motion of the spring system. (c) Find the general solution of the spring system as above assuming that there is no damping force but the external force F(t) = 4 sin(√13t) is applied to the object from its equilibrium position with no initial velocity. Describe a possible motion of the spring system. Do not solve for the unknown constants.
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