Problems of statics, angular motion and simple harmonic motion

hjkklm

All Questions are shown on pictures.

My Calculated answers:

A1(a) R= 19.21∠68.7^o N
(b) E = 19.21∠-111.34^o N or = -19.21∠68.7^o N <--- Is't either one answer is correct or not? If not, which answer is correct and why? Thanks.

A2(b) I = 0.5mr² = 1.125kgm²
A2(a) k=(I/m)^1/2 = 0.212m
A2(c) αt=ω, α = 3.14 rad/s²
A2(d) T=Iα = 3.53Nm

I can't gain the answer of A2(a) first. I use the A2(b) answer to help me to gain the A2(a) answer. So, the step of my calculated order is A2(b) -> A2(a) -> A2(c) -> A2(d). Is't correct?

B1(a)(ii) R_BY = 1500N

sum of force and moment = 0

R_A = 1200N (toward left)
R_BX = 1200N (toward right)

B1(b) R_BY = 500N
R_A = 2012.4N (toward left)
R_BX = 1146.4N (toward right)

B2(a) KE = (0.5)(10)(100) = 500J
(b) PE = (10)(9.81)(147.8) = 14503.1J
(c) v² = {[(500 + 14503.1)x2]/10}^0.5 =54.8m/s
(d ) WD = 1.2(230) = 276J , v= {[(15003.1-276)x2]/10}^0.5 = 54.3m/s


B3(a) n = 1/0.08 = 12.5Hz
(b) m = (0.08/2π)²(20x10³) = 3.24kg
(c) ω = 2π(12.5) = 78.5rad/s, v=78.54x0.01 = 0.785m/s
(d) f = 78.54²(0.006) = 37.01m/s² , T = 2π(0.006/37.01)^0.5 = 0.08s
(e) I can't do this part, may you help me, please?

All Questions are shown on pictures.
All above my calculated ans. are correct or not? It there are something wrong, please don't hesitate to correct my answers and give some comment. Thanks a lot.

Attached Thumbnails

     

hjkklm

Questions of pictures B2 and B3

Attached Thumbnails