Pulse Wave
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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\(\LaTeX\)
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Exercise:
A pulse wave is a periodical signal consisting of constant pulses. For a given period T a pulse wave is characterised by its amplitude V_ and the pulse duration tau. The duty cycle Dtau/T is the ratio of pulse duration and period. center includegraphicswidthtextwidth#image_path:pulswavno-fill-# center abcliste abc Derive a formal expression for the mean value of a pulse wave with duty cycle D. abc Derive a formal expression for the root mean square value of a pulse wave with duty cycle D. abcliste
Solution:
abcliste abc The mean value is given by V_m fracT _^T vt textdt fracT _^tau V_ textdt + fracV_ tauT V_ D abc The mean square sscVrms is given by sscV^rms fracT _^T v^t textdt fracT _^tau V_^ textdt + fracV_^ tauT V_^ D It follows for the root mean square sscVrms V_ sqrtD abcliste The figure below shows the mean and root mean square for a duty cycle DDO. The shaded area above the mean value is equal to the shaded area below for each cycle. Since the duty cycle is always less than the root mean square is always greater than the mean value. An animated version is linked to this exercise. center includegraphicswidthtextwidth#image_path:pulswav# center The graphical meaning of the root mean square can be seen in the figure below square of the signal. The shaded area above the square of the root mean square value is equal to the shaded area below for each cycle. center includegraphicswidthtextwidth#image_path:pulswavsquared-# center
A pulse wave is a periodical signal consisting of constant pulses. For a given period T a pulse wave is characterised by its amplitude V_ and the pulse duration tau. The duty cycle Dtau/T is the ratio of pulse duration and period. center includegraphicswidthtextwidth#image_path:pulswavno-fill-# center abcliste abc Derive a formal expression for the mean value of a pulse wave with duty cycle D. abc Derive a formal expression for the root mean square value of a pulse wave with duty cycle D. abcliste
Solution:
abcliste abc The mean value is given by V_m fracT _^T vt textdt fracT _^tau V_ textdt + fracV_ tauT V_ D abc The mean square sscVrms is given by sscV^rms fracT _^T v^t textdt fracT _^tau V_^ textdt + fracV_^ tauT V_^ D It follows for the root mean square sscVrms V_ sqrtD abcliste The figure below shows the mean and root mean square for a duty cycle DDO. The shaded area above the mean value is equal to the shaded area below for each cycle. Since the duty cycle is always less than the root mean square is always greater than the mean value. An animated version is linked to this exercise. center includegraphicswidthtextwidth#image_path:pulswav# center The graphical meaning of the root mean square can be seen in the figure below square of the signal. The shaded area above the square of the root mean square value is equal to the shaded area below for each cycle. center includegraphicswidthtextwidth#image_path:pulswavsquared-# center
Meta Information
Exercise:
A pulse wave is a periodical signal consisting of constant pulses. For a given period T a pulse wave is characterised by its amplitude V_ and the pulse duration tau. The duty cycle Dtau/T is the ratio of pulse duration and period. center includegraphicswidthtextwidth#image_path:pulswavno-fill-# center abcliste abc Derive a formal expression for the mean value of a pulse wave with duty cycle D. abc Derive a formal expression for the root mean square value of a pulse wave with duty cycle D. abcliste
Solution:
abcliste abc The mean value is given by V_m fracT _^T vt textdt fracT _^tau V_ textdt + fracV_ tauT V_ D abc The mean square sscVrms is given by sscV^rms fracT _^T v^t textdt fracT _^tau V_^ textdt + fracV_^ tauT V_^ D It follows for the root mean square sscVrms V_ sqrtD abcliste The figure below shows the mean and root mean square for a duty cycle DDO. The shaded area above the mean value is equal to the shaded area below for each cycle. Since the duty cycle is always less than the root mean square is always greater than the mean value. An animated version is linked to this exercise. center includegraphicswidthtextwidth#image_path:pulswav# center The graphical meaning of the root mean square can be seen in the figure below square of the signal. The shaded area above the square of the root mean square value is equal to the shaded area below for each cycle. center includegraphicswidthtextwidth#image_path:pulswavsquared-# center
A pulse wave is a periodical signal consisting of constant pulses. For a given period T a pulse wave is characterised by its amplitude V_ and the pulse duration tau. The duty cycle Dtau/T is the ratio of pulse duration and period. center includegraphicswidthtextwidth#image_path:pulswavno-fill-# center abcliste abc Derive a formal expression for the mean value of a pulse wave with duty cycle D. abc Derive a formal expression for the root mean square value of a pulse wave with duty cycle D. abcliste
Solution:
abcliste abc The mean value is given by V_m fracT _^T vt textdt fracT _^tau V_ textdt + fracV_ tauT V_ D abc The mean square sscVrms is given by sscV^rms fracT _^T v^t textdt fracT _^tau V_^ textdt + fracV_^ tauT V_^ D It follows for the root mean square sscVrms V_ sqrtD abcliste The figure below shows the mean and root mean square for a duty cycle DDO. The shaded area above the mean value is equal to the shaded area below for each cycle. Since the duty cycle is always less than the root mean square is always greater than the mean value. An animated version is linked to this exercise. center includegraphicswidthtextwidth#image_path:pulswav# center The graphical meaning of the root mean square can be seen in the figure below square of the signal. The shaded area above the square of the root mean square value is equal to the shaded area below for each cycle. center includegraphicswidthtextwidth#image_path:pulswavsquared-# center
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