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.

A body of mass m is attached to lower end of a spring whose upper end

1.	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.
Answer» Solution :`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`