The mass hanging on an elastic band moves according to the equation m(d^(2)s/dt^2)=-(mg/l)(s-L)
where s is the displacement of the mass, L is the natural length of the band and l is the constant parameter (called reference elongation). Find s as a function of time subject to the initial conditions.

s=s0, ds/st=0 when t=0

Question

The mass hanging on an elastic band moves according to the equation m(d^(2)s/dt^2)=-(mg/l)(s-L)
where s is the displacement of the mass, L is the natural length of the band and l is the constant parameter (called reference elongation). Find s as a function of time subject to the initial conditions.

s=s0, ds/st=0 when t=0

anonymous · Answer

okie here we go... can you identify which things are constant in our given equation ??

anonymous · Answer

Umm.....(mg/l)(s-L) is constant ?

anonymous · Answer

okie don't get confused ... i asked because we are going to double integrate our equation so we need to identify constants ..! i hope you are familiar with integration. .. 

constants in our equation are L natural length which won't change ,mass is constant and I constant parameter do you agree with me?

anonymous · Answer

Yep im with you now..

anonymous · Answer

and g is constant too..!

anonymous · Answer

trying now..

anonymous · Answer

okie ..!

anonymous · Answer

Sorry i cant :( (too many letters lol)

anonymous · Answer

Im assuming first parts is ds/dt

anonymous · Answer

are you still there :/

anonymous · Answer

wait for a sec..!

anonymous · Answer

Sorry.. hope i didnt sound rude (if i did i didnt mean to)

anonymous · Answer

Still processing....so basically to integrate we kinda do what you would do for a separable equation?

anonymous · Answer

Okay all good :) ....one question thought (might sound silly , this maths is way over my head)

anonymous · Answer

So right now the answer is in terms of ds/dt ..... but i integrate again so it is in terms s = something t?

anonymous · Answer

take my medal away. :( i'm really sorry but my answer is wrong .... i apologize.. 

my showed this question to my maths teacher and he said my method was wrong... 

this is not how you solve the problems of  this type.. i'm really sorry for inconvenience i caused

anonymous · Answer

@nicole05

anonymous · Answer

for the right method you should know how to solve differential equation of order two.. ..

and unfortunately i don't know how to solve differential equation of order two..

anonymous · Answer

@nicole05 i'm really sorry i didn't want to misguide you. ;(

anonymous · Answer

Of order two????? has it got anything to do with homogeneous and non-homogeneous ???

anonymous · Answer

And dont be sorry... i was completely cluesless

anonymous · Answer

oki ..and yes it has got to do with homogeneous differential  equation because we substitute something for something..! i don't know really.. you may Google it.. sorry for late reply..!