XW,ҝKG,X ( @ (//(  0/80@0?/8 0( ?G@POWOXOP?H0@/7@O_``h_hPX 0(P_oppxow_g@O/8'' 7p`o?G/7 0??H/8`/o?GOX@H0?/pOW?H/8 7OP?G/7( P0@PX@O0@ 0O @H/@' 00@@P0?'_OP@H( 7/7' ^^^^^^^^^^^^^^^^^^^^^^^^^^TeeBBBBeTT^^^^^^^eBDJ33333JJDBeZ^^^^TD33==#####==3JDBT^^^^eJ=###=3DeZ^^TB3# #=3JBZ^^T3#  #=JBT^^J# Sll #=JBZ^T# %,68??86,/@A*< ##45('.6787-9%:;*<=#$+&,--.,/01)2 3 $%&&'%($!)* ##  !"#     ??d3@sound0X.wav click.wavxTnS1MH?`ϒ/`AnYP[)*m&e&MP!6M`prs|~nNg/:<|<Z ꟅfDlQ4uŰ!a >@e!aʂ#_9LnT0e!`l 4)q`&Pb;p˂kb{KVql,>o'm(!\^5h޺JouqDM׌$")&G SWQ;!X-SUL G_ ;=e *ɝ|]>ZWI#9M$!v^[5ůA*v-9lwR|Һs+Z,K;".GmÀ͔Xm5Xn LL+ZMJmbfXʊCH!a"H.;nfߧGWфA}Nn7tϯOUUzWGrbobqy8nTHN?X~V]nq<2w= qNh֗F 'Z^njO?Wfe $j3˜ԫGmbjȹF<jD'U&Urj(ѕ}ml[HZRI W_!둹lE?spring@? xR ~mJl)w-ǹ鱝|#_37Q],e{q9̿M^-dD<(Q5`]fdN Tks1i󈴀? tM mass  =xs5a3 b(fdH@hhj(`Q0 F(к} start0+ xs5d3 b bF Ta`$0uaEhZEp2`K{X: !4x0"M ~3(q-ĤbL#J?xR1 3@h0g08 1 graphpoint xsuc3 b&(fd 0V7avalueup  >xs5cf3 b(fdH@Q@mIB/H8IaER#$E"!tz valuedown  ?xs5cf3 b(fdH@Q@("n$5I$ZHd'ۆ#font0Arial  spring [/draw_sprite_stretched(spring,-1,x,y,8,mass.y) 0000000mass cfrict0.02000000[ show_info()0000000cm1000000c springcon0.02000000cvspeed#(springcon*(100-y) -frict*vspeed)/m000000start naction_move_start00000000e action_move 0000100000000000cgraphcontroller.numpoints1000000000 action_sound00000000graphcontroller c numpoints0000000action_create_object 4 numpoints mass.y+25000000c numpoints1000000daction_if_variable numpoints70020000000000000action_kill_object00000000c numpoints000000000000000  action_font 00000000action_draw_text"friction "+string(mass.frict)4208000000action_draw_text"mass "+string(mass.m)42014300000action_draw_text*"spring"+string_format(mass.springcon,6,3)42020600000action_draw_line03507003500000ctick00000007000000000000000action_draw_linetick340tick3500000ctick10000000000000000 graphpoint  frictionup  action_sound00000000c mass.frict0.01000000 frictiondown  action_sound00000000c mass.frict-0.01000000massup  action_sound00000000cmass.m0.05000000massdown  action_sound00000000cmass.m-0.05000000springup  action_sound00000000cmass.springcon0.005000000 springdown  action_sound00000000cmass.springcon-0.005000000room0Mass, spring, damper experiment        p @``  XGame InformationX {\rtf1\ansi\ansicpg1252\deff0\deflang1033{\fonttbl{\f0\fnil\fcharset0 Arial;}{\f1\fnil Arial;}{\f2\fnil\fcharset2 Symbol;}{\f3\fnil MS Sans Serif;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\b\fs32 Mass Spring Damper Experiment \par \fs24 Tony Forster January 2006 \par \b0 May be copied with acknowledgement \par \b\fs16 (press escape to see experiment, F1 to return) \par \b0\f1\fs24 \par \f0 This experiment simulates a mass, ideal spring and friction. \par Rather than mks units, the unit of distance is the pixel and of time the step. \par \par For the mass: \par F = ma \par a = \f2 d\f0 speed/\f2 d\f0 t \par \f1 \par \f0 For the spring: \par F = springconstant x distance \par \par For the damper: \par F = frict x speed \par \par So: \par a = (springconstant x distancestretched + frict x speed)/m \par \par This is the formula in the step event for the mass, the rest length of the spring is 100 \par \pard\cf0\b\f3\fs16 Step Event: \par \b0 set variable vspeed relative to (springcon*(100-y) -frict*vspeed)/m \par \pard\cf1\f0\fs24 \par \b Questions \par \b0 1. Try different values of spring constant, mass and friction \par 2. What is the resonant frequency in cycles per step or period in steps per cycle, (graph tick marks are every 100 steps) \par 3. What happens when you double mass or spring? Quadruple it? \par 4. Try different mass start positions, does the frequency change? \par 5. What is the minimum friction to prevent overshoot? This is called critical damping. \par 6. Try negative values. What happens, what does this mean? \par 7. Can you modify the program so that the springs anchor point moves up and down? Try different frequencies below and above the resonant frequency. See the effect of damping. This is what happens when car suspension travels on a corrugated road. \par 8. The mass spring damper is an analogue of an electronic tuned circuit. What do mass, spring, damper, speed and position correspond to? \par 9. The simulation divides a continuous process up into steps, this is an approximation which introduces errors. Normally the errors are small but the simulation becomes unstable for very high friction. Try friction = 0.5 mass = 0.25 spring = 0.01. Can you explain what is happening?\f1 \par } Spritesspringmassstart graphpointvalueup valuedownSoundssound0 BackgroundsPathsScripts Fonts font0 Time LinesObjects springmassstartgraphcontroller graphpoint frictionup frictiondownmassupmassdown springup springdownRoomsroom0 Game Information Global Game Settings