Why is the tension equal to the spring force here? 
Here the block is oscillating and to solve this question I took the tention in the string to be equal to the spring force
But if that's the case a particle in the junction of the spring and the rope will expirence a net force of zero yet it still it goes up and down every oscillation
So the tention should be higher than the spring force at some intervals
But most questions like these take them to be the same value
 A: You are right, but usually we consider an ideal, massless string and same for the spring.  So that particle in the junction has zero mass. In reality the tension changes both along the spring as well as along the string so any small portion experience an acceleration due to the gradient in tension.
A: We do not solve homework problems on this site but the following should help.
Considering m accelerating, consider the forces on m alone, then consider the forces on m and the string at the connection to the spring.
Assuming a massless pulley (no inertia) and massless string the tension in the string is equal on both sides of the pulley.
A: As you seem to be having trouble with a general concept rather than asking for a homework solution, I will attempt an explanation. In an ideal situation they are equal. It takes more force, as the mass's weight carries it downwards, to stretch the spring further therefore more tension on the string.  So as spring force increases so does string tension, in fact they must be equal per Newton's third law of motion.
