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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: SHM a very good ques...
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ananth_patri (585)

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A very good ques on SHM someone plz solve it........the one who solves it correct will  be rated.....Here comes the ques...Just
Find the time of the system...
 


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karthik2007 (3349)

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Question is vague. Are the pulleys massless? No data given. We need the mass of that block

Anyway its simple. Use constraints and conserve energy to get the answer.

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ananth_patri (585)

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welll all the pulleys are massless and smooth...

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ananth_patri (585)

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and mass of the block is M so now is the ques complete???

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ananth_patri (585)

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@ karthik...u r not a JEE consultant r u??well get u r hands dirty and solve the ques...

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karthik2007 (3349)

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Doing calculations on the comp itself... so please excuse my calculation mistakes:

Since it is a conservative system:

1/2mv2+1/2kx2+2kx2 = K

mva + kxv + 4kxv = 0

ma = -5kx

a = -5kx/m

w = sqrt(5k/m)

T = 2pi sqrt(m/5k)



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ananth_patri (585)

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well i think the answer is wrong....mainly b cause in case the block moves up it is influenced only by spring below and not the left spring...note tht the left spring is not connected to the surface...

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anpm_dev (111)

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what's the answer

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anpm_dev (111)

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if for the block we consider the eqn...
Mg-kx-T =2Ma
then what we r going to consider the eqn for the spring at left
kx+2T=?

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karthik2007 (3349)

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@anand - you didn't get what I was doing. i am conserving the energy of the whole system dude.

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anpm_dev (111)

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@karthik what does 2kx^2 imply in ur first eqn

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karthik2007 (3349)

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That comes from constraints....

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oh yeah i got it ur method s correct but is the answer correct

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priyesh (1586)

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Let the equilibrium extensions in the spring connected to block be s1 & the other spring be s1/2 = s2 (say)
 
so let the mass be displaced x downwards other spring will get extended by x/2
 
conserving energy
 
1/2mv^2  -mgx + 1/2k(s1+x)^2 + 1/2k(s2+x/2)^2 = const
 
mva -mgv + ks1v + kxv + (ks2)v + kx/2 * v = 0
 
=> ma - mg + ks1 + kx + ks2 + kx/2 = 0
 
now at equilibrium mg -ks1 - ks2  = 0
 
=> mg = ks1 + ks2
 
so solving both equations
 
ma  + 3/2kx = 0
a = - 3kx/2m
 
T = 2piroot(2m/3k) 

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shyam10000bc (0)

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