Hello welcome to chafia physic. In this post i just want to share with you some problem that related with complex number and How to find a complex Number in polar Form . In this post we will also discussing about Function of complex variable with some sample question related with it. Ok first let's we start discussing about a complex number. A.Origin of Complex Number During our time in school we faced so many function and equation that describe something. Just for an example: we can describe free fall motion with quadratic equation like this. if x is t and a is -g now we can find how long a ball or a thing, fallen from initial heigth c. Now lets just focusing on quadratic equation. In this equation we can find x with abc formula, and from the abc formula we will get to value of x related with equation. Suppose we set the equation and get b quared is less than 4ac. As yo can see, in our x now containt i, where i is square root of -1. i is imaginary number, this nu
Welcome to Chafia Physic. In this post we will derrive the equation of motion of Damped Harmonic Oscillator . To derrive the equation of motion first we must draw the diagram of this motion in 1 Dimensional system. In this system as we can see. If we give the box a Force to the right, at instant spring force and friction will comes up in opposite direction with the force we gift. With Newton second Law we can write the total of Force acting on the box to be. Suppose we set x is equal to e^lamda t, we can subtitute it to differential equation. Subtitution will give us. Simplify the equation we get. Now we looking for lamda. From earlier we set x = e^lambda*t. Here we get two lambda, so x will have two solution. Because there are two solution of x, complete equation of Damped Harmonic Oscillator is sumation or superpotition of this two equation. With this equation the are three posibilities related with how big the magnitude of gamma and omega.