In circular motion, taking the direction towards the centre as positive,you would write the summation of force = ma where a is the centripetal acceleration. In Shm , you would do the same except that you have to take the direction towards the equilibrium as positive. Similarly you would write the summation of force = ma where a= w"x is the acceleration in shm. The negative sign is dropped because we have decided to take into consideration already by saying that towards the equilibrium taken to be positive.If the mass is below the x=0 , taking up as positive the equation is T"-mg =ma. If the mass is above the x=0 , taking down as positive the equation is mg - T' = ma. T" is always larger that T' as the resultant force is always directed towards x=0.
Applet link : shm and circular motion closely linked
