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]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A question regarding a spring and perhaps even energies.

**Physics Forums | Science Articles, Homework Help, Discussion**