Dampening force - find decrease in amplitude

Thread starter JoeyBob
Start date Apr 11, 2021
Tags

Amplitude decrease Force

AI Thread Summary

The discussion revolves around calculating the damping force and its effect on amplitude in a damped harmonic oscillator. The user initially calculates the damping coefficient 'b' as 0.129378 using a specific equation. However, when applying this value to a different mass of 17.7 kg, the resulting amplitude is 50%, which is inconsistent with the expected 59.6%. The user highlights that the amplitude decreases to 45.4% of its initial value, indicating a discrepancy in the calculations. The conversation emphasizes the importance of correctly applying the damping formula to achieve accurate results.

Apr 11, 2021

JoeyBob

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%?

Physics news on Phys.org

Apr 11, 2021

TSny

Science Advisor

Homework Helper

Gold Member

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

Thread 'I've come across another fluid pressure problem I don't understand'

Neglect gravity other than that of water; neglect friction. F1=ρgsh=1000*10*1*(1+4)=50000 N; F1=ρgsh=1000*10*0.1*4=4000 N; F3=50000-4000=46000 N?

View full post »

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...

View full post »

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...

View full post »