Critically damped harmonic motion
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 ...continues
**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 ...continues
find particular solution to: y'' + 6y' +9y = (-11e^(-3t)) / (t^2+1)
find particular solution to: y'' + 6y' +9y = (-11e^(-3t)) / (t^2+1)
Use Laplace transforms to find the solution of : y'' + 10y' +25y = 180exp(t) with y(0)=1 and y'(0)=1
Use Laplace transforms to find the solution of : y'' + 2y' = 24sin(2t) + 32cost(2t) with y(0)=1 and y'(0)=0
1) consider the equation (non-homogenous): Please see attachment for equation. • find its general solution • find the particular solution of this equation, satisfying the initial condition y(0)=0, y'(0)=0, y''(0)=0 2) find the general solution of the differential equation (non-homogeneous) Please ...continues
Find the fixed points and sketch trajectories in the phase plane for the system: ... using the phase portrait, examine the behaviour of solutions of this system as t→∞ when they start from (x,y)=(-1,0), and when they start from (x,y)=(-1,-1). Please see attached for full question.
Linear dependency, Wronskian and Bessel's Equation
Three problems regarding the Wronskian and solutions of a second order differential equation. Example of a question 1. Determine whether the following sets of functions are linearly dependant or independent... Please see attached. 2. Bessel's equation x²y" + xy' + (x² - n²)y = 0 where n is a constant, is a ...continues
Solve the linear Differential Equation
Solve the linear Differential Equation (see attachment) y'-y=exp(2x) y(0)=0 y"+6y'+10y=0 2yy'=1-y^2 y(0)=-2
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