A 10 kg weight is attached to a spring with constant k = 40 kg/m and subjected to an external force F(t) = 630 sin(5t). The weight is initially displaced 3 meters above equilibrium and given an upward velocity of 2 m/s. Find its displacement for t > 0, where y is the displacement of the object from its equilibrium position, measured positive upward. Note: This is an application of previous week material on Undetermined Coefficients with the forcing function form a sin(bx) A cos(bx) + B sin(bx) y(t) = =

A particle moves on the x axis with acceleration a(t)=6t-10 m/sec2 for t seconds over [0,10] with s(0)=0 and v(0)=6m/sec. Find the position and velocity at t=1 sec.

Use the method of undetermined coefficients to determine the form of a particular solution for the given equation. y'"' + 10y" – 11y=xe* + 4x What is the form of the particular solution with undetermined coefficients? Yp(x) = ] (Do not use d, D, e, E, i, or I as arbitrary constants since these letters already have defined meanings.)