Question

1/ The motion of a vibrating mass is given by d^2y/dt^2 + 8 dy/dt + 20y = 300 sin 4t. Show that the general solution of the differential equation is given by: y = e^-4t(A cos 2t + B sin 2t) + 15/13(sin 4t - 8 cos 4t)

          1/ The motion of a vibrating mass is given by
d^2y/dt^2 + 8 dy/dt + 20y = 300 sin 4t.
Show that the general solution of the differential equation is given by:
y = e^-4t(A cos 2t + B sin 2t) + 15/13(sin 4t - 8 cos 4t)

Added by George C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Manisha Sarker

Step 1

Since the right-hand side of the equation is a sinusoidal function, we assume a particular solution of the form: $$x_p(t) = C\sin(4t) + D\cos(4t)$$ Taking the first and second derivatives, we get: $$\dot{x}_p(t) = 4C\cos(4t) - 4D\sin(4t)$$ $$\ddot{x}_p(t) = Show more…

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1/ The motion of a vibrating mass is given by +8- + 20v = 300 sin 4. dt Show that the general solution of the differential equation is given by: 15 sin 4 Scos 4t ) 13 = 2 ~"(Acos 2t + Bsin 2t )