4. A forced damped harmonic oscillator is modelled by the equation 6 dt2 dt 9ysin(2t) Perform an a-priory analysis, guessing what the behaviour of the solution should be. Find the solution y(t). Chec...
Find a synchronous solution of the form Acos 2t+B sint to the given forced oscillator equation using the method of insertion, collecting terms, and matching coefficients to solve for A and B. y'"' + 2y' + 2y = 4 sin 3t, 2 = 3 A solution is y(t)=
(1 point) Consider the initial value problem d2y dy 8 +41y8 cos(2t), dt dy (0) y(0) = -2 -6 dt dt2 Write down the Laplace transform of the left-hand side of the equation given the initial conditions (sA2-8s+41)Y+2s-18 Your answer should be a function of s and Y with Y denoting the Laplace transform of the solution y. Write down the Laplace transform of the right-hand side of the equation (-8s+32)/(sA2-8s+20) Your answer should be a function of s only...
Find the equation of the plane that contains both the line with the equation x = 3 + 2t,y = t , z 8-t, and the line with the equation x = 5 + t,y = 4-t,z = 6
Find the equation of the plane that contains both the line with the equation x = 3 + 2t,y = t , z 8-t, and the line with the equation x = 5 + t,y = 4-t,z = 6
Find the general solution of the differential equation: dy/dt=(-y/t)+6. Use lower case c for constant in answer. y(t)=
Consider the differential equation: d y 6y--6 exp-2). d t 6.1 (1 mark) Find a solution of the form y(t) - Cp exp(-2t) for this differential equation, and enter the value of Cp below. You have not attempted this yet 6.2 (1 mark Any solution yh of d yh d t is of the form C exp(r t) for an appropriate value of r. What r? Remark. The general solution of the differential equation labelled (1) above is y(t) ....