The constants shouldn't be the same in both functions.cowmoo32 said:Homework Statement
The Attempt at a Solution
I know the general form should be
x1(t)=-C1sin(3t) + C2cos(3t)
x2(t)=C1sin(3t) + C2cos(3t)
cowmoo32 said:
Non-real eigenvalues are complex numbers that cannot be represented on the real number line. They are typically denoted by the letter "i" and have the form a + bi, where a and b are real numbers and i is the imaginary unit.
Non-real eigenvalues are important in solving mathematical and engineering problems that involve complex systems. They can help us understand the behavior and stability of these systems, and finding their corresponding eigenvectors can provide valuable insights into the underlying dynamics.
To solve problems involving non-real eigenvalues, we typically use the same methods as we would for real eigenvalues. This includes finding the characteristic equation, determining the eigenvalues, and finding the corresponding eigenvectors. However, we must also be familiar with complex numbers and their operations, such as conjugation and multiplication by the imaginary unit.
One common mistake is forgetting to include the imaginary unit when writing the complex eigenvalues. Another mistake is incorrectly calculating the eigenvectors by not taking into account the complex numbers. It is also important to remember that the eigenvectors for non-real eigenvalues will also be complex.
No, non-real eigenvalues can only have complex eigenvectors. This is because the corresponding eigenvectors must satisfy the eigenvalue equation, which involves complex numbers. Real eigenvectors can only exist for real eigenvalues.