Refer to the diagram - assume the weight is hanging from a ceiling (held in place at x=0) and then let go at t=0. The damper and the spring inovolved have the following coefficients KD = 100/s, Kg = m 500 N/m Write the Newton's 2nd law equation for the free-body diagram of the weight (similar to what we did in class recording), and then solve the equation (via Laplace transform) to find the displacement over time x(t). Assume m=10 kg. For simplicity, assume the approximation for the acceleration of the force of gravity is g = 10 s2 What is the final value of the displacement x(t)?
Transfer function
A transfer function (also known as system function or network function) of a system, subsystem, or component is a mathematical function that modifies the output of a system in each possible input. They are widely used in electronics and control systems.
Convolution Integral
Among all the electrical engineering students, this topic of convolution integral is very confusing. It is a mathematical operation of two functions f and g that produce another third type of function (f * g) , and this expresses how the shape of one is modified with the help of the other one. The process of computing it and the result function is known as convolution. After one is reversed and shifted, it is defined as the integral of the product of two functions. After producing the convolution function, the integral is evaluated for all the values of shift. The convolution integral has some similar features with the cross-correlation. The continuous or discrete variables for real-valued functions differ from cross-correlation (f * g) only by either of the two f(x) or g(x) is reflected about the y-axis or not. Therefore, it is a cross-correlation of f(x) and g(-x) or f(-x) and g(x), the cross-correlation operator is the adjoint of the operator of the convolution for complex-valued piecewise functions.
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