ODEs, IVPs

Find the general solution of the ODEs attached (about 10 different problems involving differential equations with constant coefficients) Solve the IVPs attached

critically damped harmonic motion ODE

This problem is an example of critically damped harmonic motion. A hollow steel ball weighing 4 pounds (mass = 1/8 slugs) is suspended from a spring. This stretches the spring 1/8 feet. The ball is started in motion from the equilibrium position with a downward velocity of 8 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) . Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. Take as the gravitational acceleration 32 feet per second per second. (Note that the positive y direction is down in this problem.) When using English units (lb, ft, etc.) you need to be a bit carefu... click for more

velocity of ping pong ball

**Just need help with question 3, answers for 1 and 2 are provided*** A ping-pong ball is caught in a vertical plexiglass column in which the air flow alternates sinusoidally with a period of 60 seconds. The air flow starts with a maximum upward flow at the rate of 7m/s and at t=30 seconds the flow has a minimum (upward) flow of rate of -3.4m/s. The ping-pong ball is subjected to the forces of gravity (-mg) where g=9.8m/s^2 and forces due to air resistance which are equal to k times the apparent velocity of the ball through the air. 1.) What is the average velocity of the air flow? You can average the velocity over one period or over a very long time -- the answer should come out... click for more

particular soltuion to ODE

find particular solution to: y'' + 6y' +9y = (-11e^(-3t)) / (t^2+1)

particular solutuion ODE

find particular solution to: y'' + 6y' +9y = (-11e^(-3t)) / (t^2+1)