Calculate Angular Frequency for Damping Motion with Mass-Spring System

[evgeniy]

A mass spring with natural angular frequency w= 3.6rad/s is placed in an environment where there is a damping force proportional to its speed. If the amplitude is reduced to 0.35 times its initial value in 12.9 s, what is the angular frequency of the dampin motion?

Can anyone help out with an equation that i should use?
It seems there is not enough info, like what is the velocity of the spring?
y(x=0,t) = Acos(w*t)?
since I know time and A.
Thanks...

 

[OlderDan]

A mass spring with natural angular frequency w= 3.6rad/s is placed in an environment where there is a damping force proportional to its speed. If the amplitude is reduced to 0.35 times its initial value in 12.9 s, what is the angular frequency of the dampin motion?

Can anyone help out with an equation that i should use?
It seems there is not enough info, like what is the velocity of the spring?
y(x=0,t) = Acos(w*t)?
since I know time and A.
Thanks...

The answer to this is in the same place as another question I just encountered

http://hyperphysics.phy-astr.gsu.edu/hbase/oscda.html

 

[thepatientmental]

To calculate the angular frequency of the damping motion in this scenario, we can use the equation:

w_d = w_n * sqrt(1 - (c/2m)^2)

where w_d is the angular frequency of the damping motion, w_n is the natural angular frequency of the mass-spring system, c is the damping coefficient, and m is the mass of the object.

In this case, we are given the natural angular frequency (w_n = 3.6 rad/s) and the time it takes for the amplitude to decrease (t = 12.9 s). However, we still need to determine the damping coefficient (c) and the mass (m) in order to solve for w_d.

To find the damping coefficient, we can use the information that the amplitude is reduced to 0.35 times its initial value. This means that the amplitude ratio (A/A_0) is 0.35, where A_0 is the initial amplitude.

We can use the equation for amplitude ratio in a damped mass-spring system:

A/A_0 = e^(-ct/2m)

Plugging in the given values, we get:

0.35 = e^(-c*12.9/2m)

Solving for c, we get:

c = -2m * ln(0.35)/12.9

Now, we need to determine the mass (m). We can use the fact that the natural angular frequency is given by:

w_n = sqrt(k/m)

where k is the spring constant. We can rearrange this equation to solve for m:

m = k/w_n^2

We are not given the spring constant, but we can find it using the given information that the amplitude is reduced to 0.35 times its initial value. We can use the equation for amplitude in an undamped system:

A = A_0 * cos(w_n*t)

Plugging in the given values, we get:

0.35 = cos(3.6*12.9)

Solving for A_0, we get:

A_0 = 0.35/cos(3.6*12.9)

Now, we can use the equation for spring constant:

k = m*w_n^2

Plugging in the values for m and w_n, we get:

k = 0.35/cos(3.6*12.9) * (3