Differential Equations Exam Review (5 of 6) - Review 4:...

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Review 4: L22-L281. (1) Use variation of parameters to find( )1vtand( )2vt(up to a constant) that form aparticular solution to the nonhomogeneous equation, given two linear independentsolutions to the corresponding homogeneous equation. (2) Find and simplify (if possible)a particular solution,( )pyt. (3) Give the general solution to the nonhomogeneousequation.()25512515;51,tttytyyt eytye′′+===2. The equation and a non-trivial solution( )1ytto the equation are given. Find a secondlinearly independent solution.
13. A mass-spring system is governed by the differential equation30yy′′+=,( )01y=,( )01y= −The initial displacement here is 1 m to the right of the equilibrium position (positive) andthe initial velocity is 1 m/sec to the left (negative).(a) Determine the equation of the motion in terms of the sine function along withits amplitude, period, natural frequency, angular frequency, phase angle(πϕπ<), and phase shift,ϕω. Specify units for each of the quantities.(b) How long does it take after release to pass through the equilibrium position?(c) Graph the equation of the motion.4. Assume that the motion of a mass-spring system with damping is governed by2290d ydybydtdt++=;( )01y=,( )01y=ϕ.

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Applied Calculus for the Managerial, Life, and Social Sciences
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