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A body of mass m is attached to lower en...

A body of mass m is attached to lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5s. Find the value of m is kg.

Text Solution

Verified by Experts

`T_(1)=3=2pisqrt((m)/(k))`
`T_(2)=5=2pisqrt((m+1)/(k))`
`(T_(1))/(T_(2))=(3)/(5)=sqrt((m)/(m+1))`
`(9)/(25)=(m)/(m+1)implies9m+9=25m`
`m=(9)/(16)kg`
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