Pneumonia is a lung infection that can be caused by various types of bacteria, viruses, fungi, or parasites. It can affect all age groups, including infants, children, and the elderly. Pneumonia in infants is often a medical emergency due to their underdeveloped immune system, making them more susceptible to lung infections. Children are also at high risk, and their symptoms can be more challenging to identify. In the elderly, risk factors such as weakened immunity and chronic diseases can increase the likelihood of contracting pneumonia. Pneumonia can spread through respiratory droplets and direct contact with infected individuals. This phenomenon makes it a particular concern, especially when variants like COVID pneumonia caused by the coronavirus, including the virus responsible for COVID-19, are present. Pneumonia is essentially a serious disease that requires prompt and appropriate medical treatment to be effectively managed. Symptoms of pneumonia include fever, cough that may...
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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