use the annihilator method to determinethe form of a particular solution for the given equation.
The homogeneous of the given equation is
The solution of the homogeneous is
Then, every solution to the given nonhomogeneous equation also satisfies
is the general solution to this homogeneous equation
Comparing (1) & (2)
On a smooth horizontal surface, a mass of m1 kg isattached to a fixed wall by a spring with spring constantk1 N/m. Another mass of m2 kg is attached to thefirst object by a spring with spring constant k2 N/m. Theobjects are aligned horizontally so that the springs aretheir natural lengths. As we showed in Section 5.6, thiscoupled mass–spring system is governed by the systemof differential equations
Let’s assume that m1 = m2 = 1, k1 = 3, and k2 = 2.If both objects are displaced 1 m to the right of theirequilibrium positions (compare Figure 5.26, page 283)and then released, determine the equations of motion forthe objects as follows:
(a)Show that x(2) satisfies the equation
(b) Find a general solution x(2) to (36).
(c) Substitute x(2) back into (34) to obtain a generalsolution for y(2)
(d) Use the initial conditions to determine the solutions,x(2) and y(2), which are the equations of motion.
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