1. APPLIED MATH FINAL STUDY GUIDE SECTION 2 Find the general solution to (4) 6 + 9 = 4 2 . 2. Set up but do not solve the following problem: \"A mass of 60 grams stretches a spring 4cm. The mass is also attached to a viscous damper that exerts a force of 10 Newtons when the velocity of the mass is 12 m/s. The mass is pulled down 4 cm below its equilibrium position and released. Fin the position u at any time t.\" Also provide the problem's initial conditions. 3. A 12-pound weight stretches a spring 8 inches. Assume that there is no damping and that the mass is acting on by an external force of 2e^-t Newtons. Find the general equation of the position u at any time t. (Note: you can disregard initial conditions.) 4. Find the LaPlace transform for the function below. 5. Find the inverse LaPlace transform for () = 6. Use the LaPlace transform to solve + 2 8 = 0, subject to the initial conditions (0) = 1 and (0) = 1. 0, 0 3 5, 3 7 0, 7 5 2 +6 . 7. Find the LaPlace transform for () = 31 () 4 () sinh( 4). 8. Find the inverse LaPlace transform for () = 9. Solve 2 = 3 3 2 4 4 1 2 +2+5 + 8 1 4 2 + 1 2 +1 . , subject to the initial conditions (0) = 0 and (0) = 0. 10. Express the solution to the given equation in terms of a convolution integral. + 4 = sin , subject to the initial conditions (0) = 1 and (0) = 0