Cross-eyed heart
Not what you're looking for?
27. y'' + 25y = sin(4t),
y(0) = 0, y'(0) = 0.
Plot the component curves and the orbit, the latter for the rectangle |y|< 0.25 and |y'|< 1.
Any surprises?
28. Hearts and Eyes: Find a solution formula for y'' + 25y = sin&(wt), where w is not equal 5. Plot the solution curve of the IVP with y(0) = y'(0), where w=4. Plot the orbit for 0< t <20 in the rectangle |y| < 0.1, -0.5 < |y'| < 0.3.
Repeat with w=1. Overlay the graphs.
Purchase this Solution
Solution Summary
The solution shows how to solve the required differential equations and provides the graphs that show an interesting behavior. The plot behavior is analyzed.
Solution Preview
Hi there!
Very cute!
Attached is the solution with the required graphs.
First let's solve the equation:
We start by first solving the homogenous equation:
Which has a characteristic equation:
So the homogenous solution is:
Since the independent term is not part of the homogenous solution, we guess a solution of the form:
Substituting it back in the equation we get:
Equating the coefficients of the cosine ...
Purchase this Solution
Free BrainMass Quizzes
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Probability Quiz
Some questions on probability
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.