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Chapter 6: Q12E (page 332)
Find a general solution for the differential equation with x as the independent variable:
The general solution for the differential equation with x as the independent variable is
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Use the annihilator method to show that ifin equation (4) and has the form (17) , thenis the form of a particular solution to equation (4).
use the annihilator method to determinethe form of a particular solution for the given equation.
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鈥搒pring system is governed by the systemof differential equations
Let鈥檚 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.
Find a general solution for the differential equation with x as the independent variable:
find a differential operator that annihilates the given function.
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