Damping Constant: Solving for b Homework

[Tylerladiesman217]

Homework Statement

I am solving for the damping constant (b). The amplitude has decreased to 80% of its original height (0.1m) after 10 oscillations. The mass is 2 kg, k is 5000 N/m, w is 50 rads/s, T = pi/25 s.

Homework Equations

x = 0.1cos(50t)
v = -5sin(50t)
a = -250cos(50t)

The Attempt at a Solution

I am not sure what equation to use, I tried
w = ((k/m)-(b^2/4(m)^2))^1/2

 

[BvU]

Helo Tyler,

With those equations you'll never be able to solve for the damping constant -- it doesn't appear !
Where do you think it should be sitting ?

 

[Tylerladiesman217]

Helo Tyler,

With those equations you'll never be able to solve for the damping constant -- it doesn't appear !
Where do you think it should be sitting ?

I'm not sure, the answer in the back of the book is 0.71 kg/s. I think that I might need to use a different formula, but I'm not sure.

 

[BvU]

What I meant is that your relevant equations feature a constant amplitude: no damping.

 

[Tylerladiesman217]

What I meant is that your relevant equations feature a constant amplitude: no damping.

Those are the equations assuming no damping. Maybe they aren't relative...

 

[BvU]

I am solving for the damping constant (b). The amplitude has decreased to 80% of its original height (0.1m) after 10 oscillations

So you can not use $x = 0.1\cos(50t)$ . The link I gave you should help you further...