Dyspnea: Symptoms, Causes, Diagnosis, Treatment
Dyspnea, or shortness of breath, can be a distressing symptom of various health conditions. Learn about its symptoms, causes, diagnosis, and treatment options to manage this breathing difficulty effectively.
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3.3 3.4 3.1
Homogeneous 3.3 3.4 3.1
Homogeneous zero 3.3 small 3.4 critical large 3.1
Homogeneous No damping 3.3 Small damping Critical damping 3.4 Large damping 3.1
Homogeneous oscillation No damping zero 3.3 oscillation w/decreasing amplitude Underdamping small Critical damping No oscillation 3.4 critical Over- damping No oscillation 3.1 large
Homogeneous From https://www.geogebra.org/m/ZzKbkvnz Note: Sign convention is opposite our convention
Homogeneous From https://www.geogebra.org/m/ZzKbkvnz Note: Sign convention is opposite our convention 0.01
From https://www.geogebra.org/m/ZzKbkvnz Note: Sign convention is opposite our convention Homogeneous
From https://www.geogebra.org/m/ZzKbkvnz Note: Sign convention is opposite our convention Homogeneous
Homogeneous From https://www.geogebra.org/m/ZzKbkvnz Note: Sign convention is opposite our convention For 0 < t < 1, ??1? > t??1? For t > 1, ??1? < t??1?
Homogeneous From https://www.geogebra.org/m/ZzKbkvnz Note: Sign convention is opposite our convention
From https://www.geogebra.org/m/ZzKbkvnz Note: Sign convention is opposite our convention Initial behavior depends on initial conditions Long-term behavior: u(t) 0 as t Homogeneous
Homogeneous oscillation No damping 3.3 oscillation w/decreasing amplitude Small damping Critical damping No oscillation 3.4 Large damping No oscillation 3.1
Homogeneous oscillation No damping zero 3.3 oscillation w/decreasing amplitude Underdamping small Critical damping No oscillation 3.4 critical Over- damping No oscillation 3.1 large
Non-Homogeneous is the steady state response when
Non-Homogeneous , then is the transient part. is the steady state response when
Non-Homogeneous Ch 3, 4: homogeneous soln Particular solution = = 3.7, 3.8 when transient soln Steady state soln/response If the homogeneous solution goes to 0 as t goes to , then the long-term behavior only depends on the steady state solution Note in this case, the initial values have almost no effect on the long-term behavior.
