Low Damping
About points...
We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
About difficulty...
We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
Question
Solution
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Exercise:
An LC oscillator has LO inductance CO capacitance and RO resistance. abcliste abc Verify that the oscillation is only weakly damped. abc Calculate the number of oscillations it takes until the amplitude has decreased to ratioO of the initial value. abc What fraction of the initial energy is left at this moment? abcliste
Solution:
abcliste abc The damping ratio for this system is zeta fracdeltadelta_c fracdeltaomega_ fracfracRLfracsqrtLC zeF fracRtimessqrtfracCL zeS Since zell the damping is very low i.e. the angular frequency and the period are close to the values of the undamped oscillation. abc The period of the undamped oscillation is T TF The envelope of the damped oscillation is given by At A_ e^-t/tau A_ e^-delta t Solving for the time leads to t -fraclnAt/A_delta fraclnA_/At LR The number of oscillations during the time t is N fractT fraclnA_/At Lpi RsqrtLC NoscF fraclnratioinvPpitimesRtimessqrtfracLC Nosc approx resultNoscP abc The energy is proportional to the square of the amplitude so fracEtE_ eratF ratio^ erat resultepercP abcliste
An LC oscillator has LO inductance CO capacitance and RO resistance. abcliste abc Verify that the oscillation is only weakly damped. abc Calculate the number of oscillations it takes until the amplitude has decreased to ratioO of the initial value. abc What fraction of the initial energy is left at this moment? abcliste
Solution:
abcliste abc The damping ratio for this system is zeta fracdeltadelta_c fracdeltaomega_ fracfracRLfracsqrtLC zeF fracRtimessqrtfracCL zeS Since zell the damping is very low i.e. the angular frequency and the period are close to the values of the undamped oscillation. abc The period of the undamped oscillation is T TF The envelope of the damped oscillation is given by At A_ e^-t/tau A_ e^-delta t Solving for the time leads to t -fraclnAt/A_delta fraclnA_/At LR The number of oscillations during the time t is N fractT fraclnA_/At Lpi RsqrtLC NoscF fraclnratioinvPpitimesRtimessqrtfracLC Nosc approx resultNoscP abc The energy is proportional to the square of the amplitude so fracEtE_ eratF ratio^ erat resultepercP abcliste
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Exercise:
An LC oscillator has LO inductance CO capacitance and RO resistance. abcliste abc Verify that the oscillation is only weakly damped. abc Calculate the number of oscillations it takes until the amplitude has decreased to ratioO of the initial value. abc What fraction of the initial energy is left at this moment? abcliste
Solution:
abcliste abc The damping ratio for this system is zeta fracdeltadelta_c fracdeltaomega_ fracfracRLfracsqrtLC zeF fracRtimessqrtfracCL zeS Since zell the damping is very low i.e. the angular frequency and the period are close to the values of the undamped oscillation. abc The period of the undamped oscillation is T TF The envelope of the damped oscillation is given by At A_ e^-t/tau A_ e^-delta t Solving for the time leads to t -fraclnAt/A_delta fraclnA_/At LR The number of oscillations during the time t is N fractT fraclnA_/At Lpi RsqrtLC NoscF fraclnratioinvPpitimesRtimessqrtfracLC Nosc approx resultNoscP abc The energy is proportional to the square of the amplitude so fracEtE_ eratF ratio^ erat resultepercP abcliste
An LC oscillator has LO inductance CO capacitance and RO resistance. abcliste abc Verify that the oscillation is only weakly damped. abc Calculate the number of oscillations it takes until the amplitude has decreased to ratioO of the initial value. abc What fraction of the initial energy is left at this moment? abcliste
Solution:
abcliste abc The damping ratio for this system is zeta fracdeltadelta_c fracdeltaomega_ fracfracRLfracsqrtLC zeF fracRtimessqrtfracCL zeS Since zell the damping is very low i.e. the angular frequency and the period are close to the values of the undamped oscillation. abc The period of the undamped oscillation is T TF The envelope of the damped oscillation is given by At A_ e^-t/tau A_ e^-delta t Solving for the time leads to t -fraclnAt/A_delta fraclnA_/At LR The number of oscillations during the time t is N fractT fraclnA_/At Lpi RsqrtLC NoscF fraclnratioinvPpitimesRtimessqrtfracLC Nosc approx resultNoscP abc The energy is proportional to the square of the amplitude so fracEtE_ eratF ratio^ erat resultepercP abcliste
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