Using Computers in Teaching Physics

Prof. Dr. Reimer Lincke

Institut für Experimentelle und Angewandte Physik

der Universität Kiel

lincke@physik.uni-kiel.de

Invited Talk, Bucharest, October 2000

Collaborators:Christian Siemers, Tim Aschmoneit, Ingo Büll, Jens Liley, Lars Wolter et.al.

Multimedia ?

Multimedia ?

Learning by Doing !

The Beginning:

Commodore 64and BASIC

(6502 ASSEMBLER)

Experiments with the Commodore 64 Interfaces at the USERPORT

The USERPORT of the C64 contained 1 byte bidirectional + 1 bit out. We used it with

a) Userport-Display b) AD-converter + 2-channel preamp c) Steppermotor- and Relay-Interface d) Digital- and Timer-Interface

AD-sampling rates were as high as 60.000 8-bit values per second.

The programs were written in Commodore-BASIC with SIMON´s BASIC for graphics:

Ci= 56576; y = PEEK(Ci+1) {for reading ADC}; POKE Ci, 64 {for switching relay}.

Experiments with the Commodore 64 Programming a Running Light

C 64 BASIC: 10 Ci= 56576 {address of USERPORT} 20 POKE Ci+3, 255 {all bits output} 30 POKE Ci+1,0 {all LED off} 40 FOR i = 0 to 7 50 DELAY [1000] {wait 1 second} 60 POKE Ci+1,2^i {switch on next LED} 70 NEXT i 80 END

128 64 32 16 8 4 2 1

USERPORT

6502 ASSEMBLER:LDA #255 LDX #96 {load X-Register}STA 56576 {all bits output} LDY #255 {load Y-Register}LDA #00 DEY {decrement Y-Register}STA 56577 {all LED off} BNE -3 {until negative}SEC {set Carry Flag} DEX {decrement X-Register}ROL 56577 {switch on one LED} BNE -8 {until negative}

BEQ -15 {roll until >128}RTS

Wait: double loop

Experiments with the Commodore 64 Studying Induction with a Falling Magnet

A bar magnet falls through 6 induction coils connected in series. Since the induced voltage is proportional to the velocity, the peaks grow linearly with time. Evaluating the areas under the peaks reproduces the fact that

for every passage.

ADC input

0)( Bi dttU

PCs under DOS

8-Bit-CardMinimal Interfaces at the Printer Port

TURBO-Pascal(Microsoft Assembler)

Experiments with PCs 8-Bit Card in a Slot

This system was centered around an 8-bit card sitting in a standard slot. It contained all the logic including two ADCs and DACs, three 16 bit timers and an 8-bit digital port. Preamplifiers, Schmitt-triggers, stepper-motor controls etc. were contained in three separate inter-face boxes.

The programming was done in TURBO PASCAL : adc1=$104; portB=$101; y:=PORT[adc1] {making one AD conversion}; PORT[portB]:=1 {switching relay #1};

Up to 50.000 8-bit values could be converted and recorded per second. Two separate ADCs and preamplifiers provided genuine 2-channel operation. Prohibiting all interrupts enabled perfect data recording.

Experiments with PCs Minimal Interfaces at the Printer Port

Modern printer ports permit most bits to be defined as input or output. This allows the construction of some extremely simple interfaces:

ADTI: 2-channel 12-bit ADC (multiplexed) with preamplifier, 2-channel digital in, 2-channel digital out, 12-bit DAC .

RMI: 4 relays (max 3A/50V), 2 stepper-motor controls.

Both interfaces can be operated simultaneously (LPT2 and extra LPT3) using Turbo Pascal.

L = 7,34 mH = 787,1 Hz

C = 5,57 µF T = 1,27 ms

RL = 4,2 = RL/2L = 286/s

R = 1 M

R

LC

(RL)

ADW

Contrary to the mechanical oscillations, here the agreement between experiment and theory is excellent.

Experiments with PCs Damped LC-Oscillations: Frequency and Decay Constant

Induction Coils

Characteristics of a Nonlinear Oscillator: The time function is not harmonic.

The period depends on the amplitude.

Experiments with PCs Wackelschwinger as Nonlinear Oscillator

Problems with Using Modern Hard- and Software in the Teaching Lab

• Modern operating systems (e.g. WINDOWS) use multitasking. This prohibits time critical measurements.

• Ports cannot be addressed directly.

• Measurement of short times (<10ms) is difficult.

• ISA-bus is too fast.

• There are too many diverging port- and bus standards.

• Programming languages (Delphi, Visual Basic, C++ etc) are very powerful and very complex. They take too much time from physics and should be left for professionals.

Serial communication

An interface for a WINDOWS system needs intelligence: only with a microcontroller can one record a series of fast equidistant AD-values. The measuring routines must be programmed in the controller‘s assembly language. A programming language suitable for calling these routines, communicating with the PC and graphing and evaluating the data is the graphical language LabView.

RS 232

Experiments under WINDOWS UNIMESS and LabView

UNIMESS and LabViewA Pair for the Physics Laboratory

Contents of the Lab

• no program code, object oriented programming

• modern software, modern techniques of communication

• frontend and program structure are produced by the student

• a wide variety of physics problems can be solved parallel to learning LabView and interfacing

Advantages

• even students without any previous knowledge of programming can master the subjects in a very short time (about 3 times faster than with TURBO Pascal)

• highly motivating by ‚instant results‘ and attractive graphics

• very low price: LabView Student Edition DM 99,-- Material for Interface DM

400,--

LabView: A Graphical Programming Language Programming an RC-Control with UNIMESS

A capacitor is charged/discharged between given limits.

Here we measure the inductance from the decay time of the current through the coil: The time constant T = L/R corresponds to a factor e-1 = 0,368, i.e. the voltage over the shunt must decay from 1900 to 699. We measure L/R = 2,82 ms. With the ohmic resistance of the

coil equal to 11,26 and the shunt equal to 2,74 , there results L = 39,5 mH. This is 5% larger than obtained from a precision measurement.

8,2

2,74

Experiments with UNIMESS Measuring L from the Decay Time

Experiments with UNIMESS and FD4EDriving an LC-Circuit with Rectangular Voltage

The program sweeps the frequency of the function generator FD4E and records the rectified signal across R.

With the function generator set to rectan-gular output, each harmonic (Ak=1/k2) produces its resonance at k times the frequency (see below). The partial waves thus are physically real, not just mathema-tical tricks!

Experiments with UNIMESS and FD4EExciting Acoustic Pipes with a -Pulse

Two cylindrical pipes are excited by discharging a capacitor through a loudspeaker.

The time signal shows damped beats. If one measures the beat frequency fs one obtains the difference between the upper and the lower frequency f+ - f - in the resonance curve.

A FOURIER analysis of the time function recovers the resonance curve.

f+

f -

fs

Experiments with UNIMESSMeasuring g with a Falling Ladder

The program records 20 times at which the light gate is opened/closed and calculates the speed and acceleration

Modelling

BASICTURBO-Pascal

MathCadLabView

Interactive PhysicsSpread Sheet Programs

Modelling with C-64 BASIC Damped Oscillations Using the EULER-Method

200 HIRES 0,1

210 DT = 1 : K=0.03

220 Y=60 : V=0 : A=0

230 FOR T=0 TO 319

240 A=-K*Y

250 REM A=A-0.02*V

260 REM A=A-0.05*SGN(V)

270 V=V+A*DT

280 Y=Y+V*DT

290 PLOT T,100-Y,1

300 NEXT T A=-K*Y-0.05*SGN(V)

The simple EULER-Method is, of course, introduced with due comments.

A=-K*Y-0.02*V

Modelling with MathCad Damped Oscillations Using the EULER-Method

A) Stokes‘ Friction B) Dry Friction

In order to update vi and xi before going to i+1, the vector concept has to be used.

Modelling with LabviewThe Radial Schrödinger-Equation of the H-Atom

n = 1 E = -13,607 eVStep 10-10 m

n = 2 E = -3,467 eVStep 2·10-10 m

n = 3 E = -1,511 eVStep 2·10-10 m

Here the Schrödinger-equation is integrated by the Euler-method using shift registers and the formula node of LabView.

When running the program, one has to adjust the energy until the wave function vanishes for r . This yields the energy eigenvalues.

Modelling with Interactive Physics Symbolic Programming of a Newtonian World

In Interactive Physics, an bject (ball, cube, spring etc.) is placed on the screen and provided with physical properties (mass, eleaticity, charge etc.) an initial conditions (position, velocity, angular rotation etc.). The program then calculates future positions and plots various diagrams. In this application, 7 speres are provided with an analytically specified interactive force containing an attractive and a repulsive term. With some damping, this suffices to build a crystal.

If the factor ´Temp´ in front of the random force is increased, the crystal will melt.

Evaluating Data with Spread Sheet Programs Measuring the Wavelength of a Laser Using a Ruler

y1

y0

0 0

y1

y0

y2

Grating

Distance Grating-Wall (cm) 354 Grating Constant (mm) 1

Order Position (cm) cos(alpha) Lambda (nm)0 11,1 0,99951 16,8 0,9989 633,02 21,0 0,9982 631,83 24,5 0,9976 631,74 27,6 0,9970 633,65 30,3 0,9964 630,46 32,8 0,9957 629,07 35,2 0,9951 630,98 37,4 0,9945 630,49 39,5 0,9938 630,710 41,5 0,9932 631,011 43,5 0,9925 634,012 45,3 0,9919 633,113 46,9 0,9913 628,514 48,7 0,9907 631,415 50,3 0,9901 630,2

Average Wavelength (nm): 631,32

The beam of a HeNe-laser falls onto the scale of a ruler. The diffracted beam hits a perpendicular plane in the positions yn

From this one calculates

d/n*(cos(0)-cos(n))

Here d is the grating constant.

This is a real experiment! Only the evaluation of the data is performed with the aid of a PC.

The spread sheet program was done with Microsoft Excel.

Control-Experiments

Some Examples

ControlTemperature Control With Peltier-Element

On/Off : 2-Point PI : Proportional/Integral

An aluminum block is standing on a PELTIER element. Its temperature t is to be stabilized to a fixed value t0. Two control mechanisms are applied: 1. On/off heating: for t < t0 full power heating, for t > t0 full power cooling. 2. PI-control: the heating current is given by

i = P ·(t-t0) + I· (t-t0)dt

ControlBalancing an Inverted Pendulum

A meter stick is mounted on a potentiometer carried by a motor-driven cart. The program keeps the tumbling stick perpendicular and the cart‘s position in the center of the track.

Nonlinear Dynamics

Modellingand

Experiments

If one adds a term in x4 to the parabolic potential of a harmonic oscillator (i.e. a cubic term to the linear force), one ends up with a DUFFING-Potential. The resulting oscillation shows the typical behaviour:

For nonlinear oszillators the period depends on the amplitude!

Nonlinear DynamicsModelling with MathCad

BMW

Wirbelstrombremse

Unwucht

Position Transducer BMW

The wellknown POHL Pendulum is a typical harmonic Oscillator used for demonstration purposes. With added excentric mass and a stepper motor it became a paradigm for the nonlinear oscillator.

PC-Interface

Nonlinear DynamicsPOHL-Pendulum

0 1

Figures: The diagrams show the angle as function of time, the velocity as function of

time and the velocity as function of angle (phase space).

Left: No eddy current brake, only mechanical damping, no motor excitation. The

pendulum was started in the extreme right position; it ends in the right potential

minimum.

Right: Excitation by stepping motor excenter, strong eddy current damping. The

oscillation is nearly harmonic, the phase diagram is similar to an ellipse.

Nonlinear DynamicsPOHL-Pendulum: Free and Driven Oscillations

Figures: In the diagrams angle as function of time and velocity as function of time, the

motor phase is shown in addition.

Left: The amplitudes of the oscillation alternate. One complete period of oscillation

corresponds to two periods of the motor; this is called Period Doubling.

Right: Four motor periods correspond to one complete oscillatory period.

2 3

Nonlinear DynamicsPOHL-Pendulum: Period Doubling and Quadrupling

A systematic variation of the damping yields the socalled Feigenbaum Diagram. This plot here

shows 100 extrema (max and min) after a transient period of 300 seconds. The marked

positions correspond to the oscillatory modes shown before:

1. Simple oscillation. 2. Period doubling. 3. Period quadrupling. 4. Chaos.

5. Window in Chaos. 6. Free oscillation.

1 2 3

4 5

6

Nonlinear DynamicsPOHL-Pendulum: Feigenbaum-Diagram

Repeated ZOOM: Self Similarity

Nonlinear DynamicsPOHL-Pendulum: Domains (left/right)

Nonlinear DynamicsMagnetic Pendulum

A steel bob swings in the field of three permanent magnets.

The position of the bob is determined by ultrasound: the bob carries a transmitter and the base plate two receivers.

Nonlinear DynamicsMagnetic Pendulum: Different Orbits

Chaotic Orbits Periodic Orbits

Quasi Periodic Orbits

Nonlinear DynamicsMagnetic Pendulum: Domains for Six Magnets

For this figure, six magnets are used. Every starting point of an oscillation of the pendulum is marked with the colour of the magnet at which the pendulum will finally come to rest.

Starting in the immerdiate neighbourhood of the red magnet, e.g., will finally cause the pendulum to rest at the red magnet, but many other stating points, too.

The structure of this map is fractal: mgnification reveals new details, and these details show self similarity.

Nonlinear DynamicsTODA-Oscillator: Circuit and Properties

If one uses a capacitive diode (BY249) rather than a normal capacitor in an RCL-circuit, then the capacitance will depend on the voltage, and the circuit is nonlinear.

The lower picture shows the energy in the capacitor as a function of charge.

The advantage of using such a TODA-Oscillator for studying nonlinear phenomena rather than the POHL-Pendulum ist its high frequency. Thus even bifurcation-diagrams can be recorded in a short time.

Diode

fixed capacitor

Nonlinear DynamicsTODA-Oscillator: Time Function

A) Udriver = 1,38V : Fundamental

B) Udriver = 3,88V : Period Doubling

The experiment is so fast that one can record many time functions for varying driving amplitudes:

C) Sequence of Poincaré-Points as Function of Driver Voltage

Some Larger Projects

Parts of Diploma or Doctoral Theses

(Often Used Commercially)

Olympic Sailing Competitions in Savannah, Ga.Computing Optimal Tacking Courses

Nuclear Physics in the Introductory Laboratory-Spectra of a Radium Source

Standard -detector: DM 1800,-- PIN-photodiode BPX 61 DM 8.50

remove cover glass

<< ADC PC

Main experiment: Energy spectra of the decay products of radium as a function of distance between source and detector: Bragg-ionization-curve of air.

Left: Energy Spectra for different distances source-detector. Right: The position of the maxima is plotted as a function of distance.

Nuclear Physics in the Introductory Laboratory-Spectra of a Radium Source