# Thread: Consider a harmonic oscillator with mass m=1 , spring constant k=7, & ...

1. ## Consider a harmonic oscillator with mass m=1 , spring constant k=7, & ...

Consider a harmonic oscillator with mass m=1 , spring constant k=7, & damping coefficient b=8

A.) write the second order differential equations and corresponding first order system
B.) find the eigenvalues and Eigenvectors of the system
C.) find the general solution
D.) find the solution that satisfies the initial conditions y(0)=-1 , v(0)=5
E.) sketch the solution curve (question d) in the (y,v) plane
F.) sketch the y(t) and v(t) graphs o the solution of the initial value problem

I have include some photos of my work, I'm pretty confident about all the parts except e & f

2. ## Re: Consider a harmonic oscillator with mass m=1 , spring constant k=7, & ...

These are correct except for (f)

The shape of y(t) is wrong. It should look like a decaying exponential, i.e. convex.

One other small thing. Generally when specifying eigenvectors, if things result in integer vector elements you'd like the first element to be 1. I.e. rather than using {-1, 7} use {1, -7}. It's a small point but it makes clearer the direction of the vector if you consistently do this.