Numerical Methods Lab Report

7/24/2019 Numerical Methods Lab Report

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Problem:

The 80 lb ball is supported from the horizontal ring using three springs each having an

unstretched length of 1.5 ft and stiffness of k = 50 lbft. !etermine the distance " from

the ring to point # for e$uilibrium.

#nal%tical &olution:

&ince the three springs are e$uidistant 'ith each other( the tensions of the three springsthen are e$ual.

"et " = stretched length

1.5

" h )*% = 0

+ F ( h L )=W

'here , = "-15

3 (50)( L−15)√ L2−(15)2

L=80

15 ( L−15 )√ L2−(15 )2

2a=8



225 ( L2

−3 L+2.25 ) ( L2

−2.25 )=64 L2

5 L4−675 L

3−64 L2+1518.75 L−1139 .0625=0

" = . ft

/umerical &olution:

5 L4−675 L

3−64 L2+1518.75 L−1139 .0625=0

teration /umber 1

,u: 1 ,l: + ,r: a: 100.002

teration /umber

,u: ,l: + ,r: .5 a: 0.002

teration /umber +

,u: ,l: .5 ,r: .5 a: 11.112

teration /umber 3

,u: ,l: .5 ,r: .15 a: 5.882

teration /umber 5

,u: .15 ,l: .5 ,r: .1845 a: .82

teration /umber

,u: .1845 ,l: .5 ,r: .188 a: 1.312

teration /umber 4

,u: .188 ,l: .5 ,r: .+33 a: 0.402



teration /umber 8

,u: .188 ,l: .+33 ,r: . a: 0.+52

teration /umber 6

,u: .188 ,l: . ,r: .4 a: 0.182

teration /umber 10

,u: .4 ,l: . ,r: .3 a: 0.062

teration /umber 11

,u: .4 ,l: .3 ,r: .+ a: 0.032

&ource 7ode:

package bisection

import static 9ava.lang.ath.

import static 9ava.lang.ath.abs

import static 9ava.lang.ath.po'

import 9ava.math.;oundingode

import 9ava.te,t.!ecimal*ormat

import 9ava.util.&canner

<< <

< author #,l ;o% 7abatana

<

public class >&7T?/ @



static &canner in = ne' &cannerA&%stem.inB

public static void mainA&tringCD argsB @ double ,r = 0( ,rEold = 0( func

!ecimal formatter

!ecimal*ormat d = ne' !ecimal*ormatAFGG.GGGGFB

d.set;oundingodeA;oundingode.H#"*EIPB

&%stem.out.printlnAF>&7T?/ TH?! JnFB

&%stem.out.printAFThe *unction is fA,B = 5"K3-45"K+-3"KL1518.45"-

11+6.05 Jn JnFB &%stem.out.printAFnter number of terations: FB

int z = in.ne,tntAB

&%stem.out.printAFnter ,l and ,u: FB

double ,u = in.ne,t!oubleAB

double ,l = in.ne,t!oubleAB

&%stem.out.printlnAFFB

for Aint i = 1 i M= z iLLB@

&%stem.out.printAFteration /umber F L i LFJnFB

,rEold = ,r

,r = A,uL,lB

func = A5<po'A,r( 3BB-A45<po'A,r(+BB-A3<po'A,r(BBLA1518.45<,rB-11+6.05

&%stem.out.printAF,u: FL d.formatA,uBB

&%stem.out.printAF ,l: F L d.formatA,lBB



if Afunc N= 0B @

,l = ,r

O else @

,u = ,r O

double # = absAA,r-,rEoldB,rB<100

&%stem.out.printAF ,r: F L d.formatA,rB L F a: FB

&%stem.out.printfAF2.fF(#B

&%stem.out.printAF2FB

&%stem.out.printlnAFJnFB O

O

O

&creenshot:

Numerical Methods Lab Report

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