Pneumonia, a serious condition involving inflammation of the lungs, can occur more frequently during the summer in countries with four seasons like China, Japan, the United States, Canada, Russia, and Central Europe. This is due to various environmental and human behavioral factors. According to case studies, mycoplasma pneumonia significantly increases with rising average temperatures and relative humidity. The main symptoms of pneumonia include difficulty breathing (shortness of breath), flu-like symptoms, fever, cough, fatigue, and chest pain. The disease can affect one or both lungs and can occur in all age groups, especially children, the elderly, and individuals with weakened immune systems who are at higher risk. Pneumonia can be classified into two types: infectious and non-infectious. Infectious pneumonia is caused by infectious agents or pathogens, such as bacteria or viruses, while non-infectious pneumonia is caused by non-infectious factors and other medical conditions....
Finding \( h(t) \) from Transfer Function \( H(s) \) Find \( h(t) \) from \( H(s) = \frac{s^2}{s^3 + 4s^2 + 4s} \) Discussion: We need to perform the inverse Laplace transform. Here are the steps to follow to obtain \( h(t) \) from the transfer function \( H(s) \): Step 1: Factorize the denominator of \( H(s) \) \[ H(s) = \frac{s^2}{s^3 + 4s^2 + 4s} = \frac{s^2}{s(s^2 + 4s + 4)} = \frac{s^2}{s(s + 2)^2} \] Step 2: Convert the fraction into a simpler partial fraction form for easier inversion \[ H(s) = \frac{s^2}{s(s + 2)^2} = \frac{A}{s} + \frac{B}{s + 2} + \frac{C}{(s + 2)^2} \] \[ s^2 = A(s + 2)^2 + Bs(s + 2) + Cs \] \[ s^2 = A s^2 + 4A s + 4A + B s^2 + 2B s + C s \] \[ s^2 = (A + B) s^2 + (4A + 2B + C) s + 4A \] Step 3: Determine the Coefficients \[ s^2 = (A + B) s^2 + (4A + 2B + C) s + 4A \] By comparing coefficients, we get: ...
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