QJEEM21Ph1f07: JEE Main 2021 Physics - Class 11 JEEM21Ph1f07 Solution: If two similar springs each of spring constant K 1 are joined…

Question

Verified Solution • 2025–26 Session moderate

If two similar springs each of spring constant K₁ are joined in series, the new spring constant and time period would be changed by a factor :

Accepted Answer

{1 \over {{K_{eq}}}} = {1 \over {{K_1}}} + {1 \over {{K_1}}}

\Rightarrow {K_{eq}} = {{{K_1} \times {K_1}} \over {{K_1} + {K_2}}} = {{K_1^2} \over {2{K_1}}} = {{{K_2}} \over 2}

\therefore

T' = 2\pi {\sqrt {{m \over {{K_{eq}}}}} }

= 2\pi {\sqrt {{m \over {{{{K_1}} \over 2}}}} }

= 2\pi {\sqrt {{{2m} \over {{K_1}}}} }

= \sqrt 2 T

[ where

T = 2\pi {\sqrt {{m \over {{K_1}}}} }

]

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