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A mass M attached to a spring oscillates...

A mass M attached to a spring oscillates with a period of 2 sec . If the mass is increased by 2 kg , the period increase by the second. Find the initial mass m assuming that Hook's law is obeyed.

Text Solution

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We know that `T=2pisqrt((M)/(k))` where k = spring constant
In first case, `2=2pisqrt((M)/(k))" "...(1)`
In second case, `3=2pisqrt((M+2)/(k))" "...(2)`
Squaring equation (1) and (2) and then dividing (2) by (1) , we have,
`(3^(2))/(2^(2))=(M+2)/(M)`
`9/4=(M+2)/(M)=1+2/M`
`9/4=1+2/M`
Solving we get , initial mass M = 1.6 kg.
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