Astudent does an experiment with a pendulum. in the first trial, she displaces the pendulum 5 cm. in the second trial, she displaces the same pendulum a distance of 10 cm. in what ways would the graphs that represent these simple harmonic motion graphs be different? in what ways would they be the same?

Well, there are different ways you can represent the motion
of the pendulum on a graph.  For example, the graph could
show the pendulum's displacement, total distance, position,
speed, velocity, or acceleration against time.  Your question
doesn't specify which quantity the graphs show, so it's pretty
tough to describe their similarities and differences, since these
could be different depending on the quantity being graphed. 

I have decided to make it simple, and assume that the graph shows
the distance away from the center against time, with positive and
negative values to represent whether its position is to the left or right
of the center.  And now I shall proceed to answer the question that
I just invented.

In both cases, the graph would be a "sine" wave.  That is, it would be
the graph of the equation 

Y = A · sin(B · time) .

' A ' is the amplitude of the wave.

' B ' is some number that depends on the frequency of the swing . . .
how often the pendulum completes one full swing.

The two graphs would have different amplitudes, so the number 'A'
would be different.  It would be 5 for the first graph and 10 on the 2nd one.

But the number 'B' would be the same for both graphs, because 
when she pulled it farther and let it go, it would make bigger swings,
but they would not happen any faster or slower than the small swings.

In the space of, say one minute, the pendulum would make the same
number of swings both times.  That number would only depend on the
length of the string, but not on how far you pull it sideways before you
let it go. 

1. may 2. september 3. february, and december4. 70°f