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Reviewing for the MCAT this Christmas, most of physics is going okay except I run into a few areas I was never familiar with to be begin with.

By what percentage does the frequency diminish in a horizontal spring mass system where k=1x10^3 N/m and m= 4 kg if the motion is dampened by a frictional force that has a damping coefficient of 2 kg/s?

k=1000 N/m

m = 4 kg

W(d)=2 kg/s

w=sqrt(K/m)

A=A(0)e-(b/2m)t

w(d)=sqrt(w^2-(b/2m)^2)

Found omega by taking the square root of 1000/4, which is 15.81. From there I plugged that into my third equation, to give me b=126.12.

Here is where I'm stuck and have been staring at this for over an hour. I know the solution is 0.0125% so I used that to work backward:

0.0125A(0)=A(0)e-(126.12/2*4)*t

and found t to be 0.57 s.

Thus, apparently if you solve for t you can solve for the percentage. But how the heck can you solve for t? No other harmonics equation gives me that number.Uhhhhgggg I never studied damped motion in HS OR college...google isn't helping, can someone else?

EDIT:

Okay. Just realized that if it's damped by 0.0125%, then I formatted my equation wrong to find time backwards. It should be

.999875(0)=A(0)e-(126.12/2*4)*t

t=7.93e-6

So this is the proper format I believe, however I'm no closer to solving for time without working backwards! Help!

## Homework Statement

By what percentage does the frequency diminish in a horizontal spring mass system where k=1x10^3 N/m and m= 4 kg if the motion is dampened by a frictional force that has a damping coefficient of 2 kg/s?

k=1000 N/m

m = 4 kg

W(d)=2 kg/s

## Homework Equations

w=sqrt(K/m)

A=A(0)e-(b/2m)t

w(d)=sqrt(w^2-(b/2m)^2)

## The Attempt at a Solution

Found omega by taking the square root of 1000/4, which is 15.81. From there I plugged that into my third equation, to give me b=126.12.

Here is where I'm stuck and have been staring at this for over an hour. I know the solution is 0.0125% so I used that to work backward:

0.0125A(0)=A(0)e-(126.12/2*4)*t

and found t to be 0.57 s.

Thus, apparently if you solve for t you can solve for the percentage. But how the heck can you solve for t? No other harmonics equation gives me that number.Uhhhhgggg I never studied damped motion in HS OR college...google isn't helping, can someone else?

EDIT:

Okay. Just realized that if it's damped by 0.0125%, then I formatted my equation wrong to find time backwards. It should be

.999875(0)=A(0)e-(126.12/2*4)*t

t=7.93e-6

So this is the proper format I believe, however I'm no closer to solving for time without working backwards! Help!

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