Page 131 - Math Grade 12 (Advance)

PROEUS DARA

ma=-k(S+x)+mg (I)
d2
n:ilru a dlf09gts4trHl.HL:lb15~6ltrHu9 stl X dl'U'i:flnJSl t~mt?!QlS :a=~
0
"
"""
1 '"IGV GV dt2

WtmtFeft : &tJtf:irl1~16i'i:f1SYlfO m = lkg ts4utl~S,fOHS'H ,fO~b156'\QlS1'Ut1tl
II it).-. I 1 1 U l.i
II I
~ f;1J ., 0 o.., •
0.20m '1 Qfl~HU1: t = o &?l<\J1~ums4:nbtLffl'l:39ff!brnstlu~ru 0.40m '1 'U~'U'i:3ntf:i
1 1
trntl ~~2J~ fit9jtl t rnt!:ll 115& 05~ S 0.70m/ s '1 ~ nfd~ffl~ ~S13 rn Sl t fL11 t S g '1

GtfW: t!:l1115Ylf0 !kg tg2J1fOHtl61QlS 0.20m &Slgff11:313J1litJint?iQ1S

1 9 8
mg = kS iJ §; k = mg = x · = 49 N . m
i.J s 0.20

2
d x k
-+-x = 0
dtz m
2
d x 49 11
- + -X = 0 'i5 X + 49 X = 0
dt2 1 "'
&f:i'titlm~b!H1.n:tnrn t = 0 ' X= 0.40m tSl8&1'=iQlS x(O) = 0.4 tUirutrn~sts4

c:P
!Hl.Jl:tnrn t = 0 ?1 0.70m/s tSlHI'=iQlS x'(O) = -0.70
&L:J1g1t\.fl11JfO{§ffl~ x" +49x = 0 ff1'1:3b15n2rt.nt~'i:3 x(O) = 0.4 sb x'(O) = -0.70
l.i B 1-a

t?!QlS A. = ±7i

m{§rugt9itsfO{§ffl~ x"+49x = 0 ~ x(t) = Acos7t+Bsin7t
GV U
ttilru x(O) = 0.4 tS18 : 0.4 = A 'i5 A = ~
"' 5
x'(t) = -7Asin7t + 7Bsin7t

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