A region in space contains a total positive charge Q that is distributed spheric

Question

A region in space contains a total positive charge Q that is distributed spherically such that the volume charge density p(r) is given by:
p(r) = for r < R/2,
p(r) = 2(1 - r/R) for R/2 < r < R
p(r) = 0 for r>R.
Here is a postive constant having units of C/m^3. a) Determine "a" in terms of Q and R. b) Using Gauss's law, derive an expression for the magnitude of "E" (Electric force) as a function of r. Do this seperately for all three regions. Express your Answer in terms of the total charge Q. Be sure to check that your results agree on the boundaries of the regions. c) What fraction of the total charge is contained within the region r < R/2? d) if an electron with charge q' = -e is oscillating back and forth about r = 0 ( the center of the distribution) with an amplitude of less than R/2, show that the is simple harmonic. e) what is the period of motion in part "d)"?
The total charge is : Q = Q1 + Q2.
Q1 = *(4/3)pi(R/2)^3 = ( pi R^3)/6 is the charge contained in the region rQ2 =(11 pi a R^3)/24
Then Q = ( pi R^3)(1/6 + 11/24) = (5/8) pi R^3
(a) = (8/5) Q/(pi R^3)
(b) E(r) = 8 Q r/(15 €o pi R^3) 0E(r) = (Q/5pi€o)[(16 r)/(3 R^3) - (4 r^2)/(R^4) - 1/(12 r^2)]
per R/2 < r < R
E(r) = Q/(4 pi €o r^2) per R(c) Q1 = (4/15) Q
(d) F = - e E = - [(8 Q e)/(15 pi €o R^3)] r = - k r
+ (k/m) r = 0
(e) T = 2 pi sqr(m/k)
I got this 2 weeks ago but now forget how can someone rewalk me through the steps and re explain what I did wrong

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