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Introduction Physics 6B Lab, The laws of physics are based on experimental and observational facts Laboratory work is therefore. an important part of a course in general physics helping you develop skill in fundamental scientific. measurements and increasing your understanding of the physical concepts It is profitable for you to. experience the difficulties of making quantitative measurements in the real world and to learn how. to record and process experimental data For these reasons successful completion of laboratory. work is required of every student,PREPARATION, Read the assigned experiment in the manual before coming to the laboratory Since each experiment. must be finished during the lab session familiarity with the underlying theory and procedure will. prove helpful in speeding up your work Although you may leave when the required work is. complete there are often additional credit assignments at the end of each write up The most. common reason for not finishing the additional credit portion is failure to read the manual before. coming to lab We dislike testing you but if your TA suspects that you have not read the manual. ahead of time he or she may ask you a few simple questions about the experiment If you cannot. answer satisfactorily you may lose mills see below. RESPONSIBILITY AND SAFETY, Laboratories are equipped at great expense You must therefore exercise care in the use of equip. ment Each experiment in the lab manual lists the apparatus required At the beginning of each. laboratory period check that you have everything and that it is in good condition Thereafter you. are responsible for all damaged and missing articles At the end of each period put your place. in order and check the apparatus By following this procedure you will relieve yourself of any. blame for the misdeeds of other students and you will aid the instructor materially in keeping the. laboratory in order, The laboratory benches are only for material necessary for work Food clothing and other personal. belongings not immediately needed should be placed elsewhere A cluttered messy laboratory. bench invites accidents Most accidents can be prevented by care and foresight If an accident does. occur or if someone is injured the accident should be reported immediately Clean up any broken. glass or spilled fluids, You are allowed some freedom in this laboratory to arrange your work according to your own taste.

The only requirement is that you complete each experiment and report the results clearly in your. lab manual We have supplied detailed instructions to help you finish the experiments especially. Physics 6B Lab, the first few However if you know a better way of performing the lab and in particular a different. way of arranging your calculations or graphing feel free to improvise Ask your TA if you are in. Each experiment is designed to be completed within the laboratory session Your TA will check off. your lab manual and computer screen at the end of the session There are no reports to submit. The lab grade accounts for approximately 15 of your course total Basically 12 points 12 are. awarded for satisfactorily completing the assignments filling in your lab manual and or displaying. the computer screen with the completed work Thus we expect every student who attends all. labs and follows instructions to receive these 12 points If the TA finds your work on a particular. experiment unsatisfactory or incomplete he or she will inform you You will then have the option. of redoing the experiment or completing it to your TA s satisfaction In general if you work on the. lab diligently during the allocated two hours you will receive full credit even if you do not finish. the experiment, Another two points 2 will be divided into tenths of a point called mills 1 point 10 mills. For most labs you will have an opportunity to earn several mills by answering questions related to. the experiment displaying computer skills reporting or printing results clearly in your lab manual. or performing some additional credit work When you have earned 20 mills two more points. will be added to your lab grade Please note that these 20 mills are additional credit not extra. credit Not all students may be able to finish the additional credit portion of the experiment. The one final point 1 divided into ten mills will be awarded at the discretion of your TA He. or she may award you 0 to 10 mills at the end of the course for special ingenuity or truly superior. work We expect these TA mills to be given to only a few students in any section Occasionally. the TA mills are used by the course instructor to balance grading differences among TAs. If you miss an experiment without excuse you will lose two of the 15 points See below for the. policy on missing labs Be sure to check with your TA about making up the computer skills you. may be responsible for them in a later lab Most of the first 12 points of your lab grade is based. on work reported in your manual which you must therefore bring to each session Your TA may. make surprise checks of your manual periodically during the quarter and award mills for complete. easy to read results If you forget to bring your manual then record the experimental data on. separate sheets of paper and copy them into the manual later However if the TA finds that your. manual is incomplete you will lose mills,In summary. Physics 6B Lab,Lab grade 12 0 points,2 0 points each for any missing labs. up to 2 0 points earned in mills of additional credit. up to 1 0 point earned in TA mills,Maximum score 15 0 points.

Typically most students receive a lab grade between 13 5 and 14 5 points with the few poorest. students who attend every lab getting grades in the 12s and the few best students getting grades. in the high 14s or 15 0 There may be a couple of students who miss one or two labs without excuse. and receive grades lower than 12 0, How the lab score is used in determining a student s final course grade is at the discretion of the. individual instructor However very roughly for many instructors a lab score of 12 0 represents. approximately B work and a score of 15 0 is A work with 14 0 around the B A borderline. POLICY ON MISSING EXPERIMENTS, 1 In the Physics 6 series each experiment is worth two points out of 15 maximum points If. you miss an experiment without excuse you will lose these two points. 2 The equipment for each experiment is set up only during the assigned week you cannot. complete an experiment later in the quarter You may make up no more than one experiment. per quarter by attending another section during the same week and receiving permission from. the TA of the substitute section If the TA agrees to let you complete the experiment in that. section have him or her sign off your lab work at the end of the section and record your score. Show this signature note to your own TA, 3 At your option If you miss a lab but subsequently obtain the data from a partner who. performed the experiment and if you complete your own analysis with that data then you. will receive one of the two points This option may be used only once per quarter. 4 A written verifiable medical athletic or religious excuse may be used for only one experiment. per quarter Your other lab scores will be averaged without penalty but you will lose any. mills that might have been earned for the missed lab. 5 If you miss three or more lab sessions during the quarter for any reason your course grade will. be Incomplete and you will need to make up these experiments in another quarter Note. that certain experiments occupy two sessions If you miss any three sessions you get an. Incomplete,Physics 6B Lab Experiment 1,Driven Harmonic Oscillator. Computer and interface,Mechanical vibrator and spring holder.

Stands etc to hold vibrator,Motion sensor,C 209 spring. Weight holder and five 100 g mass disks,INTRODUCTION. This is an experiment in which you will plot the resonance curve of a driven harmonic oscillator. Harmonic oscillation was covered in Physics 6A so we include a partial review of both the underlying. physics and the Pasco Data Studio We will continue to give fairly detailed instructions for taking. data in this first Physics 6B lab However this is the last experiment with detailed instructions on. setting up Data Studio Henceforth it will be assumed that you know how to connect the cables. to the computer and to the sensors how to call up a particular sensor and how to set up a table. graph or digit window for data taking, Hooke s Law for a mass attached to a spring states that F kx where x is the displacement. of the mass from equilibrium F is the restoring force exerted by the spring on the mass and k is. the positive spring constant If this force causes the mass m to accelerate then the equation of. motion for the mass is, Substituting for the acceleration a d2 x dt2 we can rewrite Eq 1 as. kx m d2 x dt2 2,d2 x dt2 02 x 0 3, where 0 k m is called the resonance angular frequency of oscillation Eq 3 is the differential.

equation for a simple harmonic oscillator with no friction Its solution includes the sine and cosine. functions since the second derivatives of these functions are proportional to the negatives of the. functions Thus the solution x t A sin 0 t B cos 0 t satisfies Eq 3 The parameters A and. B are two constants which can be determined by the initial conditions of the motion The natural. frequency f0 of such an oscillator is,f0 0 2 1 2 k m 4. Physics 6B Lab Experiment 1, In the simple case described above the oscillations continue indefinitely We know however that. the oscillations of a real mass on a spring eventually decay because of friction Such behavior. is called damped harmonic motion To describe it mathematically we assume that the frictional. force is proportional to the velocity of the mass which is approximately true with air friction for. example and add a damping term b dx dt to the left side of Eq 2 Our equation for the damped. harmonic oscillator becomes,kx b dx dt m d2 x dt2 5. m d2 x dt2 b dx dt kx 0 6, Physics texts give us the solution of Eq 6 and explain how it is obtained. x t A0 e bt 2m cos 1 t 7, The parameter A0 is the initial amplitude of the oscillations and is the phase angle these two con.

stants are determined by the initial conditions of the motion The oscillations decay exponentially. in time as shown in the figure below, In addition the angular frequency of oscillation is shifted slightly to. 1 k m b 2m 02 b 2m 2, Now imagine that an external force which varies cosinusoidally or sinusoidally in time is applied. to the mass at an arbitrary angular frequency 2 The resultant behavior of the mass is known as. driven harmonic motion The mass vibrates with a relatively small amplitude unless the driving. angular frequency 2 is near the resonance angular frequency 0 In this case the amplitude. Physics 6B Lab Experiment 1, becomes very large If the external force has the form Fm cos 2 t then our equation for the driven. harmonic oscillator can be written as,kx b dx dt Fm cos 2 t m d2 x dt2 9. m d2 x dt2 b dx dt kx Fm cos 2 t 10, The solution of Eq 10 can also be found in physics texts.

x t Fm G cos 2 t 11,G m2 22 02 2 b2 22 12,cos 1 b 2 G 13. The factor G in the denominator of Eq 11 determines the shape of the resonance curve which. we wish to measure in this experiment When the driving angular frequency 2 is close to the. resonance angular frequency 0 G is small and the amplitude of oscillation becomes large When. the driving angular frequency 2 is far from the resonance angular frequency 0 G is large and. the amplitude of oscillation is small, This is the curve we wish to measure in the experiment. THE QUALITY FACTOR, The sharpness of the resonance curve is determined by the quality factor or Q value Q If the. frictional force measured by the parameter b is small then Q is large and the resonance curve is. sharply peaked If the frictional force is large then Q is small and the resonance curve is broad. Physics 6B Lab Experiment 1,The general definition of Q is. Q 2 energy stored energy dissipated in one cycle 14. If the energy dissipated per cycle is small then Q is large and the resonance curve is sharply. peaked Physics texts derive the relationship between Q and the motion parameters. Q m 1 b 15, and relate Q to the sharpness of the resonance peak.

where high low is the difference in angular frequencies at which the amplitude has dropped. to 1 2 of its maximum value see Figure 4 Note that Q also controls the exponential damping. factor e bt 2m in Eq 7 and Figure 1 Using Eq 15 we can show that. e bt 2m e 1 t 2Q 17, The reciprocal of the factor which multiplies t in the exponent 2m b 2Q 1 is the time required. for the amplitude of oscillation to decay to 1 e of its initial value the so called e folding time. EXPERIMENTAL SETUP, This experiment utilizes a signal interface which drives a mechanical vibrator attached to a spring. with a mass We will measure the position of the mass by echo location using the motion sensor. sonic ranger, 1 Plug the yellow banded cable of the motion sensor into digital channel 1 of the signal interface. and the other cable into digital channel 2 From the mechanical vibrator plug the red and. black wires into the output of the signal interface. 2 Turn on the signal interface and the computer,Physics 6B Lab Experiment 1. Physics 6B Lab Manual UCLA Physics and Astronomy Department Primary authors Art Hu man Ray Waung 1 Introduction Physics 6B Lab PURPOSE The laws of physics are based on experimental and observational facts Laboratory work is therefore an important part of a course in general physics helping you develop skill in fundamental scienti c measurements and increasing your understanding of the

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