a block is acted on by a spring with a constant k and a weak force of constant magnitude f. the block is pulled distance x0 from equilbrium and released. it oscillates many times and eventually comes to rest.(the block mass is M).(adsbygoogle = window.adsbygoogle || []).push({});

1)show that the decrease of amplitude is the same for each cycle of oscillation.

2) find the number of cycles n the mass oscillates before coming to rest.

here's what i did:

w=2pi/T=sqrt(k/M)

we have kx-f=Md^2x/dt^2

we have x=Acos(wt)

where A is the amplitude.

and a=-w^2Acos(wt)

if we set t=T*n (T is the time of one cycle),n number of cycles.

then we get A(cos(2pi*n)+Mw^2cos(2pi*n))=f

from here we have: A=f/(1+Mw^2)

is this enough for the first question?

for the second question, i am kind of lost here.

i think i need to apply energies but dont know exactly how?

i mean the potential energy done by the spring is kx^2/2 and this minus the work being done by friction which is equals fx, i think that this equals the first energy potential i.e kx0^2/2, (im not sure at all it's correct) and because at the end the block is at rest kx=f, ofcourse one needs to apply t=T*n, but from here im kind of stuck, if it's even correct, is it?

for those who have kleppner's book, it's at page 196, Q4.8.

btw, the answer is n=1/4[kx0/f-1]

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# Homework Help: A question regarding a spring and perhaps even energies.

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