Question

Answer all parts of the question please!

Consider the equation one gains from considering forced oscillations applied to a damped system d2y Fo -y= m c dy k cos(wt) dt2 m dt (a) Show that yp is a particular solution where, Fo - mw2) cos(wt) c sin(wt)). Yp(t) mw2)2 c2w2 - This can be written as Fo cos(wt - n), Ур (t) — where H and n are constants, independent of time. (b) Using this particular solution and the solution to the homogeneous equation we derived in class (in terms of u and )write down the general solution y(t) (c) What happens to the general solution y(t) as t tends to infinity. (d) Thus sketch a graph of the general solution, making the long term behaviour of the system clear.

Answer 1

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