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Question

# A block of mass m is attached rigidly to a spring of stiffness k1 & touches another spring of stiffness k2 as shown in the figure. Assuming the surface is smooth, the period of oscillation of the block is

A
π[mk1+mk1+k2]
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B
2πmk1+k2
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C
π[mk1+mk2]
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D
π[mk2+mk1+k2]
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Solution

## The correct option is A π[√mk1+√mk1+k2]The block will exceute one half of SHM under the action of spring k1 alone till it touches the spring k2. The other half of SHM will be under the action of both k1 and k2 which are parallel. keq=k1+k2 Time period of first half t1=T12=12(2π√mk1)=π√mk1 & Time period of second half t2=T22=12(2π√mkeq) =π√mk1+k2 ∴ Total time period of SHM t=t1+t2 ⇒t=π[√mk1+√mk1+k2] Hence 'A' is the correct option.

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