Dampening force - find decrease in amplitude

In summary, dampening force is a force that opposes the motion of an object and causes it to lose energy and decrease in amplitude over time. It is typically measured in units of Newtons (N) or Joules per meter (J/m) and is affected by factors such as the mass of the object, its speed of motion, and the properties of the medium it is moving through. The decrease in amplitude can be calculated using the equation A = A<sub>0</sub>e<sup>-bt</sup>, where A<sub>0</sub> is the initial amplitude, b is the dampening coefficient, and t is time. To reduce the effect of dampening force, one can use materials with lower dampening
  • #1
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Homework Statement
see attached
Relevant Equations
w=sqrt((k/m)-(b/(2m))^2)

Amplitude = (Amax)e^((-b/(2m)t)
So first I tried to find b.

0.454=(0.6)e^((-b/(2*11.6)*50)

Anyways with some natural log algebra etc. I get b = 0.129378

But when I plug this into the same equation only changing mass to 17.7 kg I get 0.4998 or 50% when the answer should be 59.6%?
 

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  • #2
JoeyBob said:
Amplitude = (Amax)e^((-b/(2m)t)

0.454=(0.6)e^((-b/(2*11.6)*50)
The amplitude decreases to 45.4% of its initial value. So, the final amplitude is not .454
 

What is dampening force?

Dampening force is a type of force that acts to decrease the amplitude of an oscillating system. It is usually caused by friction or resistance within the system.

How does dampening force affect the amplitude of an oscillating system?

Dampening force decreases the amplitude of an oscillating system over time. As the system continues to oscillate, the dampening force acts against the motion, causing it to gradually lose energy and decrease in amplitude.

How can you find the decrease in amplitude caused by dampening force?

To find the decrease in amplitude caused by dampening force, you can use the equation A = A0e-bt, where A is the amplitude at a given time t, A0 is the initial amplitude, and b is the dampening coefficient. By plugging in different values for t, you can calculate the decrease in amplitude over time.

Can dampening force ever increase the amplitude of an oscillating system?

No, dampening force always acts to decrease the amplitude of an oscillating system. It works against the motion and causes the system to lose energy, resulting in a decrease in amplitude.

How can you reduce the effects of dampening force on an oscillating system?

One way to reduce the effects of dampening force on an oscillating system is to decrease the amount of friction or resistance within the system. This can be achieved by using smoother surfaces or lubricants to reduce friction, or by using materials with lower resistance. Another way is to increase the energy input into the system, which can counteract the effects of dampening force and maintain a higher amplitude.

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