According to the solution for this
It says work done by all the net forces on the block equals the potential energy of the spring at equilibrium and to calvulate work done it only considers the frictional force above the plane and the work done by gravity not work done by tension. Why tension does no work here ? Here the elongation of spring must be $0.1 m$ too.
But why is there no tension here won't the $1 kg$ block push the string and at first the spring will yield and then slowly it will oppose and tension should come.
Also why do we have to use energy analysis here why the answer comes wrong when I do by force analysis ie at equilibrium I equate force $kx$ to net force on block ie $mg sin(37°)$ - $f$ where $f$ is force of friction?