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Question

Find the time period of the oscillation of mass m in figures 12-E4 a,b,c. What is the equivalent spring constant of the pair of springs in each case ?

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Solution

(a) Equivalent spring constant,

k=k1+k2 (parallel)

T=2π mk=2π mk1+k2

(b) Let us, displace the block m towards left through displacement 'x'.

Resultant force,

F=F1+F2=(k1+k2)x

Acceleration,

(Fm)=(k1+k2)mx

Time period,

T=2π displacementAcceleration

=2π xx(k1+k2)m

=2π mk1+k2

The equivalent spring constant

k=k1+k2

(c) In series connection equivalent spring constant be k.

So, 1k=1k1+1k2=k2+k+1k1k2

K=k1k2k1+k2

T=2π mk

=2π m(k1+k2)k1k2


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