ME 402

Exercise 1.1 What is the largest decimal integer (base-10) that can be represented by a 4-bit binary number? (See Table 1.1) Write the integer in bth binary (base-!) and decimal (base-10) "rms. Binary Base 2: 1111.

1x(2^3)+1x(2^2)+1x(2^1)+1x(2^0)=15 1x(2^3)+1x(2^2)+1x( 2^1)+1x(2^0)=15

Binary Base 10: 15

Exercise 1.! #" $e had a digital ruler $ith t$ice the number " bits (%-bits instead " &-bits) $hat $uld be the reslutin " ur measurement be ($ith engineering units)?

Q=(FSR/2^m)

where m=6

(1.0/2^6)=0.0156

Q(res!"#in) wi!! $e 0.0156.

Exercise 1.& 'nsider an analg-t-digital cnerter $ith the "ll$ing prperties * +S,   1.0 / * 1!-bit reslutin What is the reslutin (in /lts) " the '?

Q=(FSR/2^m)

where m=12% FSR=1.0

(1.0/2^12)=2.1&&1&x10^('&) (1.0/2^12)=2.1&&1&x10 ^('&)

Exercise 1.2 /isit yur "arite n-line endr and search "r a cmputer (3' r ac) sund card. ,eprt the "ll$ing speci5catins A6-Series - 4GB Memory - 500GB Hard Drive  a*e an e!: HP - 15.6" Laptop - AMD A6-Series

Bla!   ,ri-e : $259.99  "i in"# res!"#in (in $i#s): n# ien  "i in"# rane (in !#s): n# ien  axim"m sam!e ra#e (in 4): n# ien Exercise !.4 'nsider the step respnse t ur car mdel (!.6) $ith the "ll$ing parameters mass  700 8g9 drag ce:cient  !!2 ;s9 and utput a ectr " elcities create a graph similar t +igure !.& t illustrate the step respnse " ur @car A. nntate the graph t sh$ the time cnstant and the steady state speed. ls9 ma8e sure t use apprpriate units "r each axis.

a#!a$ -e rm exam!e wi#h .&& -nersin a-#r. 77 m=8009 mass (*) 77 $=2259  !inear ra (;s/m) 77 Fs#e=150009 am!i#"e  s#e r-e in"#(;) 77 #=.19  n = Fs#e/$?(1'ex('##/#a"))9 77 @"re(1) 77 -!() 77 !#(##% e>n/.&&%A$.A) 77 x!a$e!(A
77 y!a$e!(AFirs#'Erers#e resnseA) 77 ri n

Exercise !.2 'nsider the step respnse t ur car mdel (!.6) $ith the parameters gien in Exercise !.4 What is the minimum step input amplitude (+-min) that $uld cause ur carB t g "rm 0-%0 mph? −∞

60 ? 0.&& =

 x 250

800

∗(1− e

225

)

  = 603&.5   

Base n #his minim"m s#e in"# am!i#"e% hw !n es i# #a*e r #he -ar #  rm 0' 60 mh nswer% $e-a"se F is #he minim"m # rea-h 60mh% an #he #ime s-a!e # rea-h 60 is in@ni#e% i# w"! #a*e an in@ni#e !en#h  #ime # rea-h 60 mh. G we "$!e Fmin w !n es i# #a*e r #he -ar #  rm 0'60 mh − x

60 ? 0.&& =

12069 225

800

∗(1− e

225

)

  = 2.1063 

Hha# is #he new # see (in mh)

−∞

  I 0.&& =

12069 225

800

∗(1− e

225

)

  = 120 J

w !n es i# #a*e r #he -ar # a-hiee #his new # see nswer # >"es#in is% #he e!-i#y an F was -a!-"!a#e er an in@ni#e #ime rane% an #herere wi!! #a*e an in@ni#e am"n#  #ime # a-hiee new # see.

Exercise !.C +rmulate a mathematical mdel " the dynamic temperature respnse " the >&2termperature sensr.  Du can assume the "ll$ing physical parameters *Speci5c eat cp  0.6 F
  Firs# rer iKeren#ia! e>"a#in exresse wi#h #he a!"es ien a$e.
T  ( t ) =

' 

T  ( t ) =

0.286

s

hA ( Tf  ( t )−T  ( t ) ) C 

( Tf  ( t )− T  ( t ) )

 "a#ins (a "n-#in) r a s#e -hane in am$ien# #emera#"re  100 L. ' 

T  ( t ) =

0.286

s

( 100 K )=28.6 K  s

  rei-#in  #he #ime -ns#an#  #he sys#em wi#h arria#e "ni#s.

Tau ( s )=

Cp h∗ A