A student hangs a 0.125 kg object on a spring, sets it into oscillation, and obt

Question

A student hangs a 0.125 kg object on a spring, sets it into oscillation, and obtains the data for the position and velocity of the object as a function of time shown in the graphs below.

On the grid below, sketch the potential energy of the object-spring-Earth system as a function of time. Explicitly label any intercepts, asymptotes, maxima, or minima with numerical values, as appropriate.

(b) On the axes below, sketch the acceleration of the object as a function of time. Explicitly label any intercepts, asymptotes, maxima, or minima with numerical values, as appropriate.

Really need this in the next 30-40 minutes if possible guys! Thanks!

1.00 0.80-- 0.60 0.20 t | 0.00 0.0 0.5 1.0 1.5 2.0 2.5 Time (s) 1.5 1.0 E 0.5 0.0 -0.5 1.0 00 0.51.0Timet6)20 2.5 0.0 0.5 1,0 1 2.0 2.5 Time (s)

Explanation / Answer

A) let spring constant, k=1

E=k*x^2/2

At t=0,x=0.5 E=0.5^2/2=0.125J

At t= 0.5.x=1 E=1/2=0.5J

At t=1,x=0.5 E=0.125J

Hence repeat itself

So, graph is of kind sine function with intercept 0.125J, maximum 1J and minimum is 0.125J.

B) as we know that acceleration,a=velocity/time

So we get same kind of graph as velocity time graph with asymptot. Intercept is 0 m/s^2

Maximum is approximately 6m/s^2 i.e. ~1.5/0.25=6

Minimum is 0 m/s^2

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