Mars

2004-Nov-17, 05:14 PM

This is for extra credit, so I don't need the answer I just want to make sure I am doing this right.

A mass of 1 slug, when attached to a spring, stretches 2 feet and then comes to rest in the equilibrium position. Starting at t=0, an external force of f(t)=e^-t*sin(4*t) is applied to the system. Find the equation of motion if the surronding medium offers a damping force numericall equal to 8 times the instantaneous velocity.

Analyze the displacements for t->infinity

So I have the equation:

x" + 8*x' + 16*x = e^-t*sin(4*t)

Am I correct this far?

I have W=mg which would be W= 1*32ft/sec

W=32

since ks=F and F=W and W=mg I get ks=32

k should = 16 because 32ft/2ft = 16

I used m^2+8*m+16=0 to find m=-4 with multiplicity 2 making

Yc=C1e^-4t+C2t*e^-4t

The rest I can get using the Superposition approach....

The other part the stumped me is the t->infinity part, I have forgotten how this goes.

Anyone help please!!

A mass of 1 slug, when attached to a spring, stretches 2 feet and then comes to rest in the equilibrium position. Starting at t=0, an external force of f(t)=e^-t*sin(4*t) is applied to the system. Find the equation of motion if the surronding medium offers a damping force numericall equal to 8 times the instantaneous velocity.

Analyze the displacements for t->infinity

So I have the equation:

x" + 8*x' + 16*x = e^-t*sin(4*t)

Am I correct this far?

I have W=mg which would be W= 1*32ft/sec

W=32

since ks=F and F=W and W=mg I get ks=32

k should = 16 because 32ft/2ft = 16

I used m^2+8*m+16=0 to find m=-4 with multiplicity 2 making

Yc=C1e^-4t+C2t*e^-4t

The rest I can get using the Superposition approach....

The other part the stumped me is the t->infinity part, I have forgotten how this goes.

Anyone help please!!