NEET Class neet Answered

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Asked by brijk456 | 12 Aug, 2019, 07:00: PM

Expert Answer

if ω is angular frequency, k is spring constant and m is the attached mass, then we have,

begin mathsize 14px style omega space equals square root of k over m end root space space o r space k space equals space omega squared m space equals space fraction numerator 4 pi squared m over denominator t squared end fraction end style

...................(1)

where t is time period of SHM

for spring-1, we have,

begin mathsize 14px style k subscript 1 equals space fraction numerator 4 pi squared m over denominator t subscript 1 superscript 2 end fraction end style

.........................(2)

for spring-2, we have,

begin mathsize 14px style k subscript 2 equals space fraction numerator 4 pi squared m over denominator t subscript 2 superscript 2 end fraction end style

.........................(3)

if two springs are connected in series, equivalent spring constant k is given by,

(1/k) = (1/k₁) + ( 1/k₂) ................... (4)

if T is time period when springs are connected in series, then using eqn.(1), (2) and (3),

we rewrite eqn.(4) as,

begin mathsize 14px style fraction numerator T squared over denominator 4 pi squared m end fraction space equals space fraction numerator t subscript 1 superscript 2 over denominator 4 pi squared m end fraction space plus space fraction numerator begin display style t subscript 2 superscript 2 end style over denominator begin display style 4 pi squared m end style end fraction space space space o r space space T squared space equals space t subscript 1 superscript 2 space plus space t subscript 2 superscript 2 end style

Answered by Thiyagarajan K | 12 Aug, 2019, 09:34: PM

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