QJEEAdv22Ph49d3: JEE Advanced 2022 Physics - Class 11 JEEAdv22Ph49d3 Solution: On a frictionless horizontal plane, a bob of mass is attached…

On a frictionless horizontal plane, a bob of mass $m=0.1 \mathrm{~kg}$ is attached to a spring with natural length $l_{0}=0.1 \mathrm{~m}$ . The spring constant is $k_{1}=0.009 \,\mathrm{Nm}^{-1}$ when the length of the spring l>l_{0} and is $k_{2}=0.016 \,\mathrm{Nm}^{-1}$ when l < l_{0} . Initially the bob is released from $l=$ $0.15 \mathrm{~m}$ . Assume that Hooke's law remains valid throughout the motion. If the time period of the full oscillation is $T=(n \pi) s$ , then the integer closest to $n$ is __________.