Download Mass-Spring System (Sol)

Math 275 Ordinary Differential Equation
In-Class Examples: Mass-Spring System
(Ex1.) A 3-kg mass is attached to a spring with stiffness k = 48 N/m. The mass is displaced ½
m to the left of the equilibrium point and given a velocity of 2 m/sec to the right. Assume the
damping force is negligible. Find the equation of motion of the mass along with the amplitude,
period, and frequency. How long after release does the mass pass through the equilibrium
position?
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(Ex2.) A ¼-kg mass is attached to a spring with stiffness 8 N/m. The damping constant for
the system is ¼ N-sec/m. If the mass is moved 1 m to the left of equilibrium and released, what
is the maximum displacement to the right that it will attain?
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(4.10.11.) A mass weighting 8lb is attached to a spring hanging from the ceiling and comes to
rest at its equilibrium position. At t = 0, an external force F (t ) = 2 cos(2t ) lb is applied to the
system. If the spring constant is 10 lb/ft and the damping constant is 1 lb-sec/ft, (a) find the
equation of motion of the mass, and (b) find the resonance frequency for the system.
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(4.10.15) An 8-kg mass is attached to a spring hanging from the ceiling and allowed to come to
rest. Assume that the spring constant is 40 N/m and the damping constant is 3 N-sec/m. At
time t = 0, an external force of fext (t ) = 2 sin(2t )cos(2t ) N is applied to the system. Determine
(a) the amplitude and (b) frequency of the steady-state solution.
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