Daten einer Schwingung
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
Short
Video
\(\LaTeX\)
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Exercise:
Lesen Sie aus dem folgen y-t-Diagramm die verlangen Daten so gut wie möglich heraus. center tikzpicturescale % Koordinatensystem draw step.grayvery thin -- grid ; draw stepgray -- grid ; draw very thick- - -- noderight ts; draw very thick- - -- node above ym; foreach x in --... draw very thick x -- x-. node below fns x; foreach y in -- draw very thick y -- .y node right fns y; % Schwingung draw domain-:very thick blue plotideTs samples x.*cos.*x-. r; tikzpicture center enumerate item Bestimmen Sie die Periode T der harmonischen Schwingung. item Bestimmen Sie die Amplitude haty der harmonischen Schwingung. item Bestimmen Sie die Phasenverschiebung varphi der harmonischen Schwingung. enumerate
Solution:
enumerate item Die Periode kann man direkt ablesen sofern man den Abstand zweier Maxima misst das ist: T apx s. item Ebenso lässt sich die Amplitude direkt ablesen. Es ist die Höhe eines Maxima also haty apx .m. item Die einzige Herausforderung stellt die Phasenverschiebung dar. Da muss man bedenkten dass die Verschiebung die in der Funktion abgelesen werden kann also .s dem Verhältnis von varphi/omega_ entspricht. Da cosomega_ t + varphi_ cosleftomega_ t + varphi_/omega_right ist. Damit gilt: .s -varphi_/omega_ myRarrow varphi_ -.s omega_ -.s fracpiT apx -. da omega_ apx .s^- ist. enumerate
Lesen Sie aus dem folgen y-t-Diagramm die verlangen Daten so gut wie möglich heraus. center tikzpicturescale % Koordinatensystem draw step.grayvery thin -- grid ; draw stepgray -- grid ; draw very thick- - -- noderight ts; draw very thick- - -- node above ym; foreach x in --... draw very thick x -- x-. node below fns x; foreach y in -- draw very thick y -- .y node right fns y; % Schwingung draw domain-:very thick blue plotideTs samples x.*cos.*x-. r; tikzpicture center enumerate item Bestimmen Sie die Periode T der harmonischen Schwingung. item Bestimmen Sie die Amplitude haty der harmonischen Schwingung. item Bestimmen Sie die Phasenverschiebung varphi der harmonischen Schwingung. enumerate
Solution:
enumerate item Die Periode kann man direkt ablesen sofern man den Abstand zweier Maxima misst das ist: T apx s. item Ebenso lässt sich die Amplitude direkt ablesen. Es ist die Höhe eines Maxima also haty apx .m. item Die einzige Herausforderung stellt die Phasenverschiebung dar. Da muss man bedenkten dass die Verschiebung die in der Funktion abgelesen werden kann also .s dem Verhältnis von varphi/omega_ entspricht. Da cosomega_ t + varphi_ cosleftomega_ t + varphi_/omega_right ist. Damit gilt: .s -varphi_/omega_ myRarrow varphi_ -.s omega_ -.s fracpiT apx -. da omega_ apx .s^- ist. enumerate
Meta Information
Exercise:
Lesen Sie aus dem folgen y-t-Diagramm die verlangen Daten so gut wie möglich heraus. center tikzpicturescale % Koordinatensystem draw step.grayvery thin -- grid ; draw stepgray -- grid ; draw very thick- - -- noderight ts; draw very thick- - -- node above ym; foreach x in --... draw very thick x -- x-. node below fns x; foreach y in -- draw very thick y -- .y node right fns y; % Schwingung draw domain-:very thick blue plotideTs samples x.*cos.*x-. r; tikzpicture center enumerate item Bestimmen Sie die Periode T der harmonischen Schwingung. item Bestimmen Sie die Amplitude haty der harmonischen Schwingung. item Bestimmen Sie die Phasenverschiebung varphi der harmonischen Schwingung. enumerate
Solution:
enumerate item Die Periode kann man direkt ablesen sofern man den Abstand zweier Maxima misst das ist: T apx s. item Ebenso lässt sich die Amplitude direkt ablesen. Es ist die Höhe eines Maxima also haty apx .m. item Die einzige Herausforderung stellt die Phasenverschiebung dar. Da muss man bedenkten dass die Verschiebung die in der Funktion abgelesen werden kann also .s dem Verhältnis von varphi/omega_ entspricht. Da cosomega_ t + varphi_ cosleftomega_ t + varphi_/omega_right ist. Damit gilt: .s -varphi_/omega_ myRarrow varphi_ -.s omega_ -.s fracpiT apx -. da omega_ apx .s^- ist. enumerate
Lesen Sie aus dem folgen y-t-Diagramm die verlangen Daten so gut wie möglich heraus. center tikzpicturescale % Koordinatensystem draw step.grayvery thin -- grid ; draw stepgray -- grid ; draw very thick- - -- noderight ts; draw very thick- - -- node above ym; foreach x in --... draw very thick x -- x-. node below fns x; foreach y in -- draw very thick y -- .y node right fns y; % Schwingung draw domain-:very thick blue plotideTs samples x.*cos.*x-. r; tikzpicture center enumerate item Bestimmen Sie die Periode T der harmonischen Schwingung. item Bestimmen Sie die Amplitude haty der harmonischen Schwingung. item Bestimmen Sie die Phasenverschiebung varphi der harmonischen Schwingung. enumerate
Solution:
enumerate item Die Periode kann man direkt ablesen sofern man den Abstand zweier Maxima misst das ist: T apx s. item Ebenso lässt sich die Amplitude direkt ablesen. Es ist die Höhe eines Maxima also haty apx .m. item Die einzige Herausforderung stellt die Phasenverschiebung dar. Da muss man bedenkten dass die Verschiebung die in der Funktion abgelesen werden kann also .s dem Verhältnis von varphi/omega_ entspricht. Da cosomega_ t + varphi_ cosleftomega_ t + varphi_/omega_right ist. Damit gilt: .s -varphi_/omega_ myRarrow varphi_ -.s omega_ -.s fracpiT apx -. da omega_ apx .s^- ist. enumerate
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