Differential equation questions

1. Find a general solution of the ODE 29\" + 5y' + 4x = 0 (the independent variable is t). 2. Solve the IVP as\" + 143' + 493 : 0, y(0) = 6, y'(0) = 5 (the independent variable is t). 3. A mechanical unit consists of a 100 kg platform on the top of a shock absorber with the spring constant 24000 N /m. (a) Draw a diagram depicting this system. Introduce the variables and show the correspond- ing units. Write down a differential equation governing the motion of this system in the absence of damping and external forces. (b) Suppose that at the initial time t = 0, the platform is 20 cm above the equilibrium position1 moving down at 2 m/sec. Determine the equation of motion. (c) Calculate the amplitude. period and frequency of the motion. Remember to include the appropriate units