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So in the case of Nyquist diagram I would use $$\frac{k}{s^{m}+sc_{v}+c_{p}}$$ to do the analysis?

Thank you that is what I have been trying the only part that I am missing is the actual transfer function. Since u=-ky once I apply the Laplace transform the only variables are Y(s). Is this wrong? Do I apply first the Laplace transform, calculate the transfer function and the substitute u=-ky?

I see what you mean, but I try to understand it using root locus because I find it very intuitive and easy visually once the plot is made to determine the renge of k where the system is stable. However, in this case I am not use which the transfer function is to use the formula 1+kG(s) to...

I apologise it was meant to be ##my''+c_vy'+c_py=c_pu##. I understand what you say, but the goal is to find the range of k wt which the system reamains stable. Other than considering the point (-1,0) in the Nyquist the number of encirclements help to determine the stability, thus the Root locus...

I have used root locus before but my confusion now is that the input is the negative feedback. Usually when I have negative feedback I consider the the error between the input (ideal) signal and the observed signal. Also, in this case what is the tranfer function since u = -k*y, and what does...

Hello I am studying mechanics and I have been reading about having the reference frame fixed at a certain point, body fixed and also the gyro equations. I an identify the gyro case easily as I am looking for an AAC body which rotates about an axis. I am confused about the other two cases in...

Hello, I am trying to get some intuition about the direction of the shear stress caused by the Hertz contact pressure. Once I exert some pressure downwards on a spherical object the direction of the Hertz pressure will be upwards. However, this case some shear stress to exist, but I can't see...

When I use Lagrange to get the equations of motion, in order to find the equilibrium conditions I set the parameters q as constants thus the derivatives to be zero and then calculate the q's that satisfy the equations of motion obtained. In ordert to check about stability I think I need to add...

I see, but when can I use the two planes method?

Initially, I calculate the moment of inertia of of a square lamina (x-z plane). Thr this square is rotated an angle $\theta$ about a vertex and I need to calculate the new moment of inertia about that vertex. Can I split the rotated square to two squares in the x-z plane and y-z plane to find...

I will try to explain it better, cause I see it's a bit confusing. When I have a rigid body like a pencil of length 2L, the generalized coordinates defined are x,y,z (COM relative to (0,0)) and $$\theta, \phi$$ (Euler's angles). However, x,y,z can be expressed as functions of $$\theta,\phi$$...

I think I undeerstand Lagrangian mechanics but I have a question that will help to clarify some concepts. Imagine I throw a pencil. For that I have 5 generalised coordinates (x,y,z and 2 rotational). When I express Kinetic Energy (T) as: $$T = 1/2m\dot{x^{2}}+1/2m\dot{y^{2}}+1/2m\dot{z^{2}} +...

Hello, I know it might sound silly but sometimes I get confused. Let's say I have a gyro-compass and I get 3 equations of torque for the 3 axes. I am expected to find the equation of motion and two of them are equated with 0. These are the Euler's dynamics equation with moving reference frame...

Hello, I am doing some contact mechanics and I had an example in my Lecture notes about a simple thrust bearing with three balls where the bottom plate is stationary, the top plate rotates with angular velocity w, and the cage rotates with angular speed Ω. It says by inspection Ω =w/2 but I...

By considering the trolley, string and mass, the external forces are the weights and the reaction force but the weight and reaction force for the trolley have no effect in the cross product to callculate Q, since r_a - r_p (p is the centre of mass of trolley) is parallel to the direction of F_i...

Yes the sphere is hanging below the trolley. I see, I have been trying to calcualte the rate of change of angular momentum (torque) using: ##\dot{\vec{h_{a}} + \dot{\vec{r_{a}}x p = Q,## ##\Q = sum_{n=i}^\n (r_{i} - r_{p}) x F_{i} ,## PS:sorry for the equations, if someone can fix it , that...

So I have a trolley of mass m that moves on a straight line. A sphere of mass m, is attached on the trolley with a light string of length a and it is left to oscillate. Just to give some idea of their positions: r_trolley = xi r_sphere = (x-asinθ)i - acosθj (θ is the angle between the string...