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![[Post New]](/templates/default/images/icon_minipost_new.gif) 23 Jan 2008 11:21:19 IST
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three identical springs each of spring constant k are connected to a mass m as shown . thn wht is the time period of the oscillation if the mass m is displaced by x along one of the springs ?
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"your future depends on what u do in present"
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23 Jan 2008 11:27:20 IST
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F net = F + F cos 60 + Fcos 60
so , k'= k + (k/4) + (k/4)
so k'= 3k / 2
Hence time period is 2 pie [under square root ( 2 m / 3 k)] .
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Ken
From: UNITED STATES, Green Bay, Wisconsin
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23 Jan 2008 11:31:02 IST
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bt ken the ans given is [2pie sqrt(m/2k)]...
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23 Jan 2008 11:36:39 IST
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ok here's the soln
got confused
the displacement of the other two springs will not be x but will be x cos 60
so
fnet = kx+k(2xcos 60) cos 60
(F cos 60)
so net k is 3k/2
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23 Jan 2008 11:42:22 IST
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if block m is displaced by dx downwards,,, the upper spring will be displaced bye dx and the lower two springs will be displaced by dx cos60 = dx/2 Net force ma = -(kdx + kdx/2 + kdx/2) = -2kdx a = -2k/m dx Hence, w^2 = 2k/m w = rt(2k/m) T=2  rt(m/2k) |
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23 Jan 2008 11:48:14 IST
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when the block is disturbed in any direction by a displacement x the due to the symmetry of the system the all the spring will exert force in the same direction and all the displacements of the springs will be equal
let the block be displaced by x towards A
on resolving the forces in the directions as shown in the fig the net force = 2kx
ma = 2kx
=> x/a = m/2k
so T = 2 pi sqrt(m/2k)
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~ANSHUMAN
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23 Jan 2008 12:00:03 IST
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thnx fr the soln's guyzz...
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23 Jan 2008 12:02:04 IST
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I think the answer is wrong....however brilliant might the illustrations be given
k' = kx + (2kx Cos 60) Cos 60
So k' = 3k/2
Hence time period = 2   (2m/3k)
Only Apurv is correct
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23 Jan 2008 12:09:48 IST
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bt yaar... u say tht k' = kx + "(2kxcos 60) cos 60 " ...hwz tht .???
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23 Jan 2008 12:25:58 IST
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See guys i am at school and so its not possible to give a detailed explanation,
i am in a hurry However, take one of them to be constant and so let that be kx
Now the net restoring force = [(kx/2)2 + (kx/2)2 + 2
(kx/2)(kx/2)Cos 120]
So resultant force = kx/2
Net restoring force is thus kx + kx/2 = 3kx/2
Hence t = 2 (2m/3k)
I am pretty certain that this answer is correct.
t  2 (m/2k )
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From J.R.R. Tolkien's 'The Lord of the Rings':
All that is gold does not glitter
Not all who wander are lost
The old that is strong does not wither,
Deep roots are not reached by frost.
From ashes a fire shall be woken
From shadows a light shall spring
Renewed shall be blade that's broken
The crown less again shall be king. |
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