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(Solved): Consider the initial value problem my^('')+cy^(')+ky=F(t),y(0)=0,y^(')(0)=0 per meter, and the appli ...
Consider the initial value problem
my^('')+cy^(')+ky=F(t),y(0)=0,y^(')(0)=0
per meter, and the applied force in Newtons is
F(t)={(30 if 0<=t<=(\pi )/(2),),(0 if t>(\pi )/(2.)):}
a. Solve the initial value problem, using that the displacement y(t) and velocity y^(')(t) remain continuous when the applied force is discontinuous.
For 0<=t<=(\pi )/(2),y(t)=
For t>(\pi )/(2),y(t)=
(c)
b. Determine the long-term behavior of the system. Is \lim_(t->\infty )y(t)=0 ? If it is, enter zero. If not, enter a function that approximates y(t) for very large positive values of t.
For very large positive values of t,y(t)~~
help (formulas)