Aspring with a spring constant of 1200 n/m has a 55-g ball at its end. the energy of the system is 5.5j. what is the amplitude of vibration?

The energy of the system is E=5.5 J. This energy is the  same at every moment of the oscillation. When the stretch x of the spring is maximum (so, when the stretch is equal to the amplitude: x=A) the velocity of the spring is zero, so all this energy is just elastic potential energy of the spring:

From which we find