Free Damped Motion: 2-lb force stretches spring 1 ft

[MarkSA]

Hello,

Q: A force of 2lbs stretches a spring 1ft. A mass weighing 3.2lbs is attached to the spring, and the system is immersed in a medium that offers a damping force numerically equal to 0.4 times the instantaneous velocity.
a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilib position.

We just started doing these and i'm having trouble getting started. I think the form should be:
my'' + By' + ky = 0
{ y(0)=-1, y'(0)=0 }

m=1/16 slugs, B=0.4, and i'm thinking k=5.2. I'm not sure where to take it from here though. Appreciate any help.

 

[Deleted member 4993]

Hello,

Q: A force of 2lbs stretches a spring 1ft. A mass weighing 3.2lbs is attached to the spring, and the system is immersed in a medium that offers a damping force numerically equal to 0.4 times the instantaneous velocity.
a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilib position.

We just started doing these and i'm having trouble getting started. I think the form should be:
my'' + By' + ky = 0
{ y(0)=-1, y'(0)=0 }

m=1/16 slugs, B=0.4, and i'm thinking k=5.2. I'm not sure where to take it from here though. Appreciate any help.

I get

k = 1/2

m = 3.2/32 = 0.1 slugs

B = 0.4

y" + Py + Q = 0

(D + r[sub:a6ca3kmz]1[/sub:a6ca3kmz])(D + r[sub:a6ca3kmz]2[/sub:a6ca3kmz]) = 0

then the homogeneous solution is:

y = A[sub:a6ca3kmz]1[/sub:a6ca3kmz]e[sup:a6ca3kmz]r[sub:a6ca3kmz]1[/sub:a6ca3kmz]t[/sup:a6ca3kmz] + A[sub:a6ca3kmz]2[/sub:a6ca3kmz]e[sup:a6ca3kmz]r[sub:a6ca3kmz]2[/sub:a6ca3kmz]t[/sup:a6ca3kmz]