A mass m attached to a spring oscillates with a period 2s. If the mass is increased by 2kg, the period increases by 1s. Find the initial mass m, asssuming that Hooke's law is obeyed.

Explanation

As, `T=2pisqrt((m)/(k))`
Case `(i)` `T=2s, m=m`
Then `2=2pisqrt((m)/(k)) or k=(4pi^(2)m)/(4)=pi^(2)m`
Case `(ii)` `T=(2+1)=3s,m=(m+2)`
Then `3=2pisqrt((m+2)/(k))=2pisqrt((m+2)/(pi^(2)m))=2sqrt((m+2)/(m))`
or `9m=4m+8 or 5m=8 or m=8//5 =1.6kg`