1.1. Figure 1 shows one cycle of the displacement-time graphs for two mass-spring systems X and Y that are performing simple harmonic motion. 

Figure 1

The springs used in oscillators X and Y have the same spring constant. 

Using information from Figure 1, determine the relation between the mass used in oscillator Y and that in oscillator X.

1.2. Explain briefly how would you use one of the graphs in Figure 1 to confirm that the motion is simple harmonic.

1.3. Figure 2 shows how the potential energy of oscillator Y varies with displacement. 

Figure 2

Draw on Figure 2: 

(i) A graph to show how the kinetic energy of the mass used in oscillator Y varies with its displacement. Label this A. 

(ii) A graph to show how the kinetic energy of the mass used in oscillator X varies with its displacement. Label this B.

1.4. Use data from the graphs to determine the spring constant of the springs used.