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The spring viewed as a input-output linear system in the way the example wants to show it is indeed a system that maps trajectories (inputs) into forces (outputs). In this sense I think my explanation is far more consistent that the current one. Can we have an explanation that rescue the best of both
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However I think the current version is really confusing. You reverted the changes based on the idea that I was introducing a different y(t). But that is :not the case if you look at the two equations that use y_1 and y_2. If you think the linear spring as the linear system, then these y_1 and y_2 are
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The article says a linear system "can be described" by a linear operator H that maps x(t) to y(t). But the article doesn't say HOW the linear operator H is used to describe the system, and it doesn't say what x(t) represents or what y(t) represents (other than calling them the "input" and the
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the :applied forces and that was exactly the y(t) I introduced. Additionally the condition "Letting y(t) = 0" is completely unnecessary and indeed confusing... What is the output then? if it is supposed to be always 0?
295:"output" which is uninformative). Does x(t) represent the state of the system? Does y(t) represent the state of the system? How do I find x(t+1) given x(t)? The rest of the article never even mentions H again.
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745:"Linear system" has a wide usage in mathematics and does not specify this particular application, The usual term is "linear systems analysis" or a little more precisely, "linear systems-analysis".
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AT MINIMUM the article needs a physical example of a linear system using the same notation H, x(t), and y(t).
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This was recently posted to my talk page. I would appreciate some help from other editors in resolving this.
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Don’t understand this section. Any chance of expanding to explain the reasoning?
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For example, a forced harmonic oscillator obeys the differential equation:
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Not all linear systems are causal. Not all causal systems are linear.
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626:{\displaystyle H(x(t))=m{\frac {d^{2}(x(t))}{dt^{2}}}+kx(t)}
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Thank you for reviewing my changes to linear systems
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