- #1

gramentz

- 16

- 0

If I have a force that is pushing upwards on a spring-mass system, and I basically have to find an equation that will give me the velocity and y-position for any given t, how much does that differ from the general form of Asin ([tex]\omega[/tex]t +[tex]\phi[/tex])?

This is what I know:

m= 2

k= 32

Vertical position y of mass: dy/dt = v

Velocity of the mass: dv/dt = f(t)/M - (k/M) * y

I know the external force is f(t) is 10sin([tex]\omega[/tex]t)

I know that y(0) and v(0) are zero.

I have to find the position and velocities when [tex]\omega[/tex]= 2, 3, 3.5, 4, 4.5, 5 rad sec and I have to use 40,000 time steps (totaling 25 seconds) where each step is 0.000625.

I know that the "preferred" frequency of the system will be at 4 rad/ sec, using [tex]\omega[/tex]= [tex]\sqrt{\frac{k}{m}}[/tex]

This is where I am having a bit of trouble: I found that when I'm examining 2 rad/sec, that v'' = 5cos2t - 16y', or that v'' = 5cos2t-16v. What I'm trying to do, is find the velocity and position of this system for any given value of t.

I was told that I can use the "general" solution of this type: v= A cos 2t + B cos 4t + C sin 2t + D sin 4t.

Am I in the right direction? Any insight would be appreciated. Thanks in advance!