A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes simple harmonic oscillations with a time period T . If the mass is inc

Question

A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes simple harmonic oscillations with a time period T . If the mass is increased by m , then the time period becomes ( 4 5 ​ T ) . The ratio of M m ​ is

TestHub · Accepted Answer

T = 2 π K M ​ ​ and T 1 ​ = 2 π K M + m ​ ​ or T T 1 ​ ​ = M M + m ​ ​ or 4 5 ​ = ( 1 + M m ​ ) 2 1 ​ or M m ​ = 16 25 ​ − 1 = 16 9 ​ ( ∵ T 1 ​ = 4 5 ​ T )

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