Match second-order differential equations with their y(t) graph

[Dusty912]

Homework Statement

The problem is in the picture. #17
I would have typed it but there are graphs that are needed for solving it. Basically trying to figure out which y(t) graph belongs to one of the sinusoidal forced equations with various parameters.

Homework Equations

euler's formula e^it=cost +isint

polar form of complex numbers

The Attempt at a Solution

so I have been complexifying the right hand side, using the guess and check method with a substituted αe^wit. Once I find α I convert it into its polar form and then change y particular so I can see it's amplitude. This along with 2π/w for the period. Am I going about this the wrong way?

 

[Mark44]

Homework Statement

The problem is in the picture. #17
I would have typed it but there are graphs that are needed for solving it. Basically trying to figure out which y(t) graph belongs to one of the sinusoidal forced equations with various parameters.

Homework Equations

euler's formula e^it=cost +isint

polar form of complex numbers

The Attempt at a Solution

so I have been complexifying the right hand side, using the guess and check method with a substituted αe^wit. Once I find α I convert it into its polar form and then change y particular so I can see it's amplitude.

This doesn't seem like a good approach to me. You're given the parameters for six different versions of the DE. For each of the six problems, substitute in the parameters, after which you should be able to tell, at least qualitatively, which of the six graphs is most appropriate. There should be a section in your textbook that talks about systems that are overdamped, underdamped, and critically damped. Some of the graphs definitely fit some or all of these categories.

This along with 2π/w for the period. Am I going about this the wrong way?