Find the motion of the mass-spring system modeled by the ODE and the initial conditions and determine the solution value when t = 3 to three decimal places. y" +25y= 24 sint, y(0) = 1, y' (0) = 1

Find the position function of a particle that travels along the x-axis for t >= 0 with acceleration of a(t)=8t-5 where the velocity at t=2 is 6 in/sec and the initial position at time t=0 is -4 inches

Solve: y" - y' – 12y - 48t + 44 y(0) = - 8, - 8, y'(0) = 23 y(t) =

The position at time t is greater than or equal to 0 of a particle moving along a coordinate line is given by s(t)=t^3+(3/2)t^2-6t a) Calculate the velocity and acceleration at time t b) Find the acceleration at each time the velocity is 0 c) When is the particle moving forward? When is it moving backwards?