# Calculate Angular Frequency for Damping Motion with Mass-Spring System

• evgeniy
In summary, a mass spring with a natural angular frequency of 3.6rad/s experiences a damping force proportional to its speed. If the amplitude is reduced to 0.35 times its initial value in 12.9 s, the angular frequency of the damping motion can be calculated using the equation y(x=0,t) = Acos(w*t), where time and amplitude are known.
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...

evgeniy said:
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

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

## 1. What is angular frequency in a mass-spring system?

The angular frequency in a mass-spring system is a measure of the rate at which the system oscillates back and forth. It is represented by the Greek letter omega (ω) and is equal to 2π times the frequency of the motion.

## 2. How do you calculate the angular frequency for damping motion in a mass-spring system?

The angular frequency for damping motion in a mass-spring system can be calculated using the equation ω = √(k/m), where k is the spring constant and m is the mass of the object. This equation takes into account the effects of damping on the motion of the system.

## 3. What is the relationship between angular frequency and period in a mass-spring system?

The period of a mass-spring system is the time it takes for one complete oscillation. The relationship between angular frequency (ω) and period (T) is T = 2π/ω. This means that as the angular frequency increases, the period decreases and vice versa.

## 4. How does changing the mass or spring constant affect the angular frequency in a mass-spring system?

Changing the mass or spring constant will directly affect the angular frequency in a mass-spring system. As the mass increases, the angular frequency decreases, and as the spring constant increases, the angular frequency increases.

## 5. Can the angular frequency in a mass-spring system be negative?

No, the angular frequency in a mass-spring system cannot be negative. It is always a positive value that represents the rate of oscillation of the system. A negative value would indicate that the system is oscillating in the opposite direction, which is not physically possible.

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