The main part of your conclusion should state what effects the spring constant and the mass of the oscillator have on the characteristics of the motion of the mass. From your description, the square of the time T for one cycle of the motion should be directly porportional to both the mass value and the spring constant. That is, if the mass is doubled, T squared should double. If the mass is tripled, t squared should triple also. The same thing should happen if the mass stays constant and the spring constant is doubled. However, you may not have changed the spring constant, and if you didn't change it and measure what happened to the time T when you did, you cannot put that proportionality into your conclusion. Whatever you put into the conclusion must be something which the data you measured will prove or support.
From measuring the spring constant, if you made repeated measurements of the amount of spring stretch for different mass values, your data should show that the amount of stretch of the spring is directly proportional to the weight-force and thus to the mass value. The weight force is g, the acceleration of gravity (from your textbook) multiplied by whatever the mass value. If a 100 gm mass stretched the spring by a length L from its resting location, then a 200 gm mass should stretch it a distance of 2L, and a 300 gm mass should stretch it by 3L. If your data does not show such proportional changes, then the "spring constant" would not be constant.
So another part of your conclusion should be what your data showed about how the spring stretch-to-mass value ratio stayed constant for all the mass values used. The proportionalities may not be perfect because of measurement errors. Any such errors should also be told about in your conclusion, if they have not already been stated earlier in the report in another section than the conclusion section.