Home » Archimedes archive » Archimedes World » AW-1996-07.adf » !Ignotum_Ignotum » !Ignotum/Formulae/Osci
!Ignotum/Formulae/Osci
This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.
Some of these files were originally commercial releases in the 1980s and 1990s, but they are now widely available online. I assume that copyright over them is no longer being asserted. If you own the copyright and would like files to be removed, please contact me.
| Tape/disk: | Home » Archimedes archive » Archimedes World » AW-1996-07.adf » !Ignotum_Ignotum |
| Filename: | !Ignotum/Formulae/Osci |
| Read OK: | ✔ |
| File size: | 06CA bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
# Physics > Oscillations a=-ks/m For simple harmonic motion, where: a=acceleration k='spring' constant m=mass of object s=displacement from equilibrium position s=Acos(wt) For simple harmonic motion, where: s=displacement from equilibrium position A=amplitude of movement w=angular velocity t=time w�=k/m For simple harmonic motion, where: w=angular velocity k='spring' constant m=mass of object T=2PI/w For simple harmonic motion, where: T=time for one period PI=3.141592654 w=angular velocity T=2PI(m/k)^� For simple harmonic motion, where: T=time for one period PI=3.141592654 m=mass of object k='spring' constant f=1/T For simple harmonic motion, where: f=frequency of oscillation T=time for one period f=w/2PI For simple harmonic motion, where: f=frequency of oscillation w=angular velocity PI=3.141592654 f=((k/m)^�)/2PI For simple harmonic motion, where: f=frequency of oscillation k='spring' constant m=mass of object PI=3.141592654 vmax=wA For simple harmonic motion, where: vmax=maximum velocity w=angular velocity A=amplitude of oscillation amax=w�A For simple harmonic motion, where: amax=maximum acceleration w=angular velocity A=amplitude of oscillation KE=�mv� Where: KE=kinetic energy of oscillator m=mass of oscillator v=velocity of oscillator PE=�ks� For simple harmonic motion, where: PE=potential energy of oscillator k='spring' constant s=displacement of oscillator from the equilibrium position E=�kA� For simple harmonic motion, where: E=total energy of oscillator k='spring' constant A=amplitude of oscillation Q=2PI(ES/EL) Where: Q=quality factor of oscillator PI=3.141592654 ES=energy stored in oscillator EL=energy lost per oscillation
00000000 23 20 50 68 79 73 69 63 73 20 3e 20 4f 73 63 69 |# Physics > Osci| 00000010 6c 6c 61 74 69 6f 6e 73 0a 61 3d 2d 6b 73 2f 6d |llations.a=-ks/m| 00000020 0a 46 6f 72 20 73 69 6d 70 6c 65 20 68 61 72 6d |.For simple harm| 00000030 6f 6e 69 63 20 6d 6f 74 69 6f 6e 2c 20 77 68 65 |onic motion, whe| 00000040 72 65 3a 0a 61 3d 61 63 63 65 6c 65 72 61 74 69 |re:.a=accelerati| 00000050 6f 6e 0a 6b 3d 27 73 70 72 69 6e 67 27 20 63 6f |on.k='spring' co| 00000060 6e 73 74 61 6e 74 0a 6d 3d 6d 61 73 73 20 6f 66 |nstant.m=mass of| 00000070 20 6f 62 6a 65 63 74 0a 73 3d 64 69 73 70 6c 61 | object.s=displa| 00000080 63 65 6d 65 6e 74 20 66 72 6f 6d 20 65 71 75 69 |cement from equi| 00000090 6c 69 62 72 69 75 6d 20 70 6f 73 69 74 69 6f 6e |librium position| 000000a0 0a 73 3d 41 63 6f 73 28 77 74 29 0a 46 6f 72 20 |.s=Acos(wt).For | 000000b0 73 69 6d 70 6c 65 20 68 61 72 6d 6f 6e 69 63 20 |simple harmonic | 000000c0 6d 6f 74 69 6f 6e 2c 20 77 68 65 72 65 3a 0a 73 |motion, where:.s| 000000d0 3d 64 69 73 70 6c 61 63 65 6d 65 6e 74 20 66 72 |=displacement fr| 000000e0 6f 6d 20 65 71 75 69 6c 69 62 72 69 75 6d 20 70 |om equilibrium p| 000000f0 6f 73 69 74 69 6f 6e 0a 41 3d 61 6d 70 6c 69 74 |osition.A=amplit| 00000100 75 64 65 20 6f 66 20 6d 6f 76 65 6d 65 6e 74 0a |ude of movement.| 00000110 77 3d 61 6e 67 75 6c 61 72 20 76 65 6c 6f 63 69 |w=angular veloci| 00000120 74 79 0a 74 3d 74 69 6d 65 0a 77 b2 3d 6b 2f 6d |ty.t=time.w.=k/m| 00000130 0a 46 6f 72 20 73 69 6d 70 6c 65 20 68 61 72 6d |.For simple harm| 00000140 6f 6e 69 63 20 6d 6f 74 69 6f 6e 2c 20 77 68 65 |onic motion, whe| 00000150 72 65 3a 0a 77 3d 61 6e 67 75 6c 61 72 20 76 65 |re:.w=angular ve| 00000160 6c 6f 63 69 74 79 0a 6b 3d 27 73 70 72 69 6e 67 |locity.k='spring| 00000170 27 20 63 6f 6e 73 74 61 6e 74 0a 6d 3d 6d 61 73 |' constant.m=mas| 00000180 73 20 6f 66 20 6f 62 6a 65 63 74 0a 0a 54 3d 32 |s of object..T=2| 00000190 50 49 2f 77 0a 46 6f 72 20 73 69 6d 70 6c 65 20 |PI/w.For simple | 000001a0 68 61 72 6d 6f 6e 69 63 20 6d 6f 74 69 6f 6e 2c |harmonic motion,| 000001b0 20 77 68 65 72 65 3a 0a 54 3d 74 69 6d 65 20 66 | where:.T=time f| 000001c0 6f 72 20 6f 6e 65 20 70 65 72 69 6f 64 0a 50 49 |or one period.PI| 000001d0 3d 33 2e 31 34 31 35 39 32 36 35 34 0a 77 3d 61 |=3.141592654.w=a| 000001e0 6e 67 75 6c 61 72 20 76 65 6c 6f 63 69 74 79 0a |ngular velocity.| 000001f0 0a 54 3d 32 50 49 28 6d 2f 6b 29 5e bd 0a 46 6f |.T=2PI(m/k)^..Fo| 00000200 72 20 73 69 6d 70 6c 65 20 68 61 72 6d 6f 6e 69 |r simple harmoni| 00000210 63 20 6d 6f 74 69 6f 6e 2c 20 77 68 65 72 65 3a |c motion, where:| 00000220 0a 54 3d 74 69 6d 65 20 66 6f 72 20 6f 6e 65 20 |.T=time for one | 00000230 70 65 72 69 6f 64 0a 50 49 3d 33 2e 31 34 31 35 |period.PI=3.1415| 00000240 39 32 36 35 34 0a 6d 3d 6d 61 73 73 20 6f 66 20 |92654.m=mass of | 00000250 6f 62 6a 65 63 74 0a 6b 3d 27 73 70 72 69 6e 67 |object.k='spring| 00000260 27 20 63 6f 6e 73 74 61 6e 74 0a 66 3d 31 2f 54 |' constant.f=1/T| 00000270 0a 46 6f 72 20 73 69 6d 70 6c 65 20 68 61 72 6d |.For simple harm| 00000280 6f 6e 69 63 20 6d 6f 74 69 6f 6e 2c 20 77 68 65 |onic motion, whe| 00000290 72 65 3a 0a 66 3d 66 72 65 71 75 65 6e 63 79 20 |re:.f=frequency | 000002a0 6f 66 20 6f 73 63 69 6c 6c 61 74 69 6f 6e 0a 54 |of oscillation.T| 000002b0 3d 74 69 6d 65 20 66 6f 72 20 6f 6e 65 20 70 65 |=time for one pe| 000002c0 72 69 6f 64 0a 0a 0a 66 3d 77 2f 32 50 49 0a 46 |riod...f=w/2PI.F| 000002d0 6f 72 20 73 69 6d 70 6c 65 20 68 61 72 6d 6f 6e |or simple harmon| 000002e0 69 63 20 6d 6f 74 69 6f 6e 2c 20 77 68 65 72 65 |ic motion, where| 000002f0 3a 0a 66 3d 66 72 65 71 75 65 6e 63 79 20 6f 66 |:.f=frequency of| 00000300 20 6f 73 63 69 6c 6c 61 74 69 6f 6e 0a 77 3d 61 | oscillation.w=a| 00000310 6e 67 75 6c 61 72 20 76 65 6c 6f 63 69 74 79 0a |ngular velocity.| 00000320 50 49 3d 33 2e 31 34 31 35 39 32 36 35 34 0a 0a |PI=3.141592654..| 00000330 66 3d 28 28 6b 2f 6d 29 5e bd 29 2f 32 50 49 0a |f=((k/m)^.)/2PI.| 00000340 46 6f 72 20 73 69 6d 70 6c 65 20 68 61 72 6d 6f |For simple harmo| 00000350 6e 69 63 20 6d 6f 74 69 6f 6e 2c 20 77 68 65 72 |nic motion, wher| 00000360 65 3a 0a 66 3d 66 72 65 71 75 65 6e 63 79 20 6f |e:.f=frequency o| 00000370 66 20 6f 73 63 69 6c 6c 61 74 69 6f 6e 0a 6b 3d |f oscillation.k=| 00000380 27 73 70 72 69 6e 67 27 20 63 6f 6e 73 74 61 6e |'spring' constan| 00000390 74 0a 6d 3d 6d 61 73 73 20 6f 66 20 6f 62 6a 65 |t.m=mass of obje| 000003a0 63 74 0a 50 49 3d 33 2e 31 34 31 35 39 32 36 35 |ct.PI=3.14159265| 000003b0 34 0a 76 6d 61 78 3d 77 41 0a 46 6f 72 20 73 69 |4.vmax=wA.For si| 000003c0 6d 70 6c 65 20 68 61 72 6d 6f 6e 69 63 20 6d 6f |mple harmonic mo| 000003d0 74 69 6f 6e 2c 20 77 68 65 72 65 3a 0a 76 6d 61 |tion, where:.vma| 000003e0 78 3d 6d 61 78 69 6d 75 6d 20 76 65 6c 6f 63 69 |x=maximum veloci| 000003f0 74 79 0a 77 3d 61 6e 67 75 6c 61 72 20 76 65 6c |ty.w=angular vel| 00000400 6f 63 69 74 79 0a 41 3d 61 6d 70 6c 69 74 75 64 |ocity.A=amplitud| 00000410 65 20 6f 66 20 6f 73 63 69 6c 6c 61 74 69 6f 6e |e of oscillation| 00000420 0a 0a 61 6d 61 78 3d 77 b2 41 0a 46 6f 72 20 73 |..amax=w.A.For s| 00000430 69 6d 70 6c 65 20 68 61 72 6d 6f 6e 69 63 20 6d |imple harmonic m| 00000440 6f 74 69 6f 6e 2c 20 77 68 65 72 65 3a 0a 61 6d |otion, where:.am| 00000450 61 78 3d 6d 61 78 69 6d 75 6d 20 61 63 63 65 6c |ax=maximum accel| 00000460 65 72 61 74 69 6f 6e 0a 77 3d 61 6e 67 75 6c 61 |eration.w=angula| 00000470 72 20 76 65 6c 6f 63 69 74 79 0a 41 3d 61 6d 70 |r velocity.A=amp| 00000480 6c 69 74 75 64 65 20 6f 66 20 6f 73 63 69 6c 6c |litude of oscill| 00000490 61 74 69 6f 6e 0a 0a 4b 45 3d bd 6d 76 b2 0a 57 |ation..KE=.mv..W| 000004a0 68 65 72 65 3a 0a 4b 45 3d 6b 69 6e 65 74 69 63 |here:.KE=kinetic| 000004b0 20 65 6e 65 72 67 79 20 6f 66 20 6f 73 63 69 6c | energy of oscil| 000004c0 6c 61 74 6f 72 0a 6d 3d 6d 61 73 73 20 6f 66 20 |lator.m=mass of | 000004d0 6f 73 63 69 6c 6c 61 74 6f 72 0a 76 3d 76 65 6c |oscillator.v=vel| 000004e0 6f 63 69 74 79 20 6f 66 20 6f 73 63 69 6c 6c 61 |ocity of oscilla| 000004f0 74 6f 72 0a 0a 50 45 3d bd 6b 73 b2 0a 46 6f 72 |tor..PE=.ks..For| 00000500 20 73 69 6d 70 6c 65 20 68 61 72 6d 6f 6e 69 63 | simple harmonic| 00000510 20 6d 6f 74 69 6f 6e 2c 20 77 68 65 72 65 3a 0a | motion, where:.| 00000520 50 45 3d 70 6f 74 65 6e 74 69 61 6c 20 65 6e 65 |PE=potential ene| 00000530 72 67 79 20 6f 66 20 6f 73 63 69 6c 6c 61 74 6f |rgy of oscillato| 00000540 72 0a 6b 3d 27 73 70 72 69 6e 67 27 20 63 6f 6e |r.k='spring' con| 00000550 73 74 61 6e 74 0a 73 3d 64 69 73 70 6c 61 63 65 |stant.s=displace| 00000560 6d 65 6e 74 20 6f 66 20 6f 73 63 69 6c 6c 61 74 |ment of oscillat| 00000570 6f 72 20 66 72 6f 6d 20 74 68 65 0a 65 71 75 69 |or from the.equi| 00000580 6c 69 62 72 69 75 6d 20 70 6f 73 69 74 69 6f 6e |librium position| 00000590 0a 45 3d bd 6b 41 b2 0a 46 6f 72 20 73 69 6d 70 |.E=.kA..For simp| 000005a0 6c 65 20 68 61 72 6d 6f 6e 69 63 20 6d 6f 74 69 |le harmonic moti| 000005b0 6f 6e 2c 20 77 68 65 72 65 3a 0a 45 3d 74 6f 74 |on, where:.E=tot| 000005c0 61 6c 20 65 6e 65 72 67 79 20 6f 66 20 6f 73 63 |al energy of osc| 000005d0 69 6c 6c 61 74 6f 72 0a 6b 3d 27 73 70 72 69 6e |illator.k='sprin| 000005e0 67 27 20 63 6f 6e 73 74 61 6e 74 0a 41 3d 61 6d |g' constant.A=am| 000005f0 70 6c 69 74 75 64 65 20 6f 66 20 6f 73 63 69 6c |plitude of oscil| 00000600 6c 61 74 69 6f 6e 0a 0a 51 3d 32 50 49 28 45 53 |lation..Q=2PI(ES| 00000610 2f 45 4c 29 0a 57 68 65 72 65 3a 0a 51 3d 71 75 |/EL).Where:.Q=qu| 00000620 61 6c 69 74 79 20 66 61 63 74 6f 72 20 6f 66 20 |ality factor of | 00000630 6f 73 63 69 6c 6c 61 74 6f 72 0a 50 49 3d 33 2e |oscillator.PI=3.| 00000640 31 34 31 35 39 32 36 35 34 0a 45 53 3d 65 6e 65 |141592654.ES=ene| 00000650 72 67 79 20 73 74 6f 72 65 64 20 69 6e 20 6f 73 |rgy stored in os| 00000660 63 69 6c 6c 61 74 6f 72 0a 45 4c 3d 65 6e 65 72 |cillator.EL=ener| 00000670 67 79 20 6c 6f 73 74 20 70 65 72 20 6f 73 63 69 |gy lost per osci| 00000680 6c 6c 61 74 69 6f 6e 0a 0a 0a 0a 0a 0a 0a 0a 0a |llation.........| 00000690 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a |................| * 000006c0 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a |..........| 000006ca
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