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Q.

In the given figure, the block is attached with a system of three ideal springs A, B, C. The block is displaced by a small distance x from itsequilibrium position vertically downwards and released. T represents the time period of small vertical oscillations of the block. Then (pulleysare ideal)

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a

T=2π11m2k

b

the deformation of the spring A is (2/11) times the displacement of the block.

c

the deformation of the spring C is (1/11) times the displacement of the block

d

the deformation of the spring B is (4/11) times the displacement of the block.

answer is A.

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Detailed Solution

Let elongation in spring A, B and C be x1, x2 and x3 respectively. Considering spring forces and constraint relationsx2=4x3 … (i) x2=2x1 … (ii) and x1+2x2+x3=x … (iii) ⇒x1=211x;x2=411x;x3=111xAlso, F=2Kx11⇒T=2π11m2k

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In the given figure, the block is attached with a system of three ideal springs A, B, C. The block is displaced by a small distance x from itsequilibrium position vertically downwards and released. T represents the time period of small vertical oscillations of the block. Then (pulleysare ideal)