MrYouMath
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If you take the Laplace transform of the system you obtain: $$msV_0(s)+FV_0(s)=U(s)$$ $$U(s)=K\left[V_0(s)-V_\text{r}(s) \right]$$ Plug the second equation into the first equation and solve for $... View answer 1 answers 0 votes 108 views Accepted answer 2 votes The examples in which it is useful are already given in your PDF file. The first reason is modal decomposition (use$x=Vz$, in which$V$is the matrix containing the eigenvectors of the matrix$A$). ... View answer 2 answers 0 votes 79 views 0 votes You did answer both questions correctly. You could also consider solving the both questions by using the Hurwitz criterion. The first one is directly solvable with the Hurwitz criterion the second one ... View answer 1 answers 1 votes 433 views 1 votes Normally you would apply Kelvin's circulation theorem on the whole system such that everything that is important is enclosed by the contour for all times$t$(note, that the author also expanded the ... View answer 1 answers 1 votes 282 views Accepted answer 1 votes The circulation is given by $$\Gamma = \oint_{C(t)}\boldsymbol{u}d\boldsymbol{r}.$$ Now, take the material derivative of this expression (remember to use the product rule because our contour is time-... View answer 1 answers 0 votes 499 views 1 votes You can use the following block diagram. Note that your$\boldsymbol{D}=\boldsymbol{0}$. If you really want to have all the states you could draw it like the following picture. You can neglect all ... View answer 2 answers 4 votes 75 views 4 votes As you might already know your system is nonlinear, which means that it is not trivial at all. See below for the plot of the system. The linearization around$(0,0)$gives you the information that the ... View answer 2 answers 1 votes 182 views 3 votes A linear state space model is given by $$\dot{\mathbf{x}}=\mathbf{A}\mathbf{x}+\mathbf{B}\mathbf{u},$$ in which$\mathbf{x}=[x_1,x_2,\ldots,x_n]^T$. The reason why we write it in matrix notation is ... View answer 1 answers 0 votes 2k views Accepted answer 2 votes Your system is open loop stable as the poles are at$s=-1$,$s=-3$and$s=0$. Note, that if the order of the pole at$s=0$is greater then 1, then the open loop system is also unstable. But closing ... View answer 3 answers 0 votes 91 views Accepted answer 2 votes The volume$V$needed to cover the surface is equal to the spherical shell volume with$d_{\text{inner}}=5 \text{ inch}=0.127\text{ m}$and$d_{\text{outer}}=d_{\text{inner}}+2\cdot 35 \cdot 10^{-9}\...

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Euler's buckling is the behavior of static loads and not time-dependent loads. You would need to look at nonstatic beam deflections but I doubt that instantaneous loading will prevent buckling. In ...

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Your goal is to move the electrons in a neuron with a magnetic field. If we assume a homogeneous magnetic field $\mathbf{B}$, then this will generate an electrodynamic force $$\mathbf{F}=q\mathbf{v}\... View answer 3 answers 1 votes 1k views 1 votes Assuming a very long cylinder (to neglect effects at the top and bottom of the cylinder) with a small wall thickness t (to assume that the stress is constant across the thickness of the wall) and ... View answer 1 answers 1 votes 177 views Accepted answer 0 votes What is the joint angle velocity? The joint angle velocity is the angular velocity of you joint, because we are acutally dealing with a 2D problem. This will become clear if you look at your ... View answer 3 answers 13 votes 1k views 11 votes Beryllium oxide is a very good electrical insulator but at the same time the best non-metal (except diamond) thermal conductor. So to summarize. In general, good thermal conductivity is correlated ... View answer 1 answers 2 votes 50 views 1 votes As @SolarMike pointed out the acoustic waves might harm the fish because the sonic speed in water is approximate 1484 \frac{\text{m}}{\text{s}} (at 20° \text{ C}), this is quite high compared to ... View answer 2 answers 0 votes 73 views 1 votes The problem that you describe comes from the fact that you calculating the average of the vector with numerical values. In order to calculate the exact mean of \sin(x) or other functions, you should ... View answer 2 answers 0 votes 2k views 2 votes First, create the free body diagram for this system. If you cut through the spring k_1 and the damper b_1 you will get two forces F_{k_1}=k_1(x_i-x_0) and F_{b_1}=b_1(\dot{x}_i-\dot{x}_0) ... View answer 3 answers 1 votes 280 views 1 votes The main idea of the hydraulic press is that we use a piston for which we have to apply a small force F_1 and small area A_1 to displace a specific volume of the incompressible fluid. Imagine we ... View answer 1 answers 0 votes 5k views Accepted answer 3 votes The force required F_{\text{r}} for driving a wheeled vehicle with mass m is given the following formula (I will neglect slip):$$F_{\text{r}}=F_{\text{tire}}+F_{\text{aero}}+F_{\text{acc.}}+F_{\...

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I think you did mix this up with proportional feedback. The transfer function is given by $$G(s)=K\frac{(s+5)(s-4)}{(s+10)(s+6)(s+3)},$$ in which $K$ is a parameter that needs to be determined. ...

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Secondary flow can result from obstacles, viscosity effects and because of changes in the size and orientation of the cross section. In general these causes lead to nonvanishing convective terms in ...

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The resolution depends on the material you are using and the frequency $f$ applied. An approximation for the resolution is given by half of the wavelength $$\lambda = \frac{c}{f}.$$ The sonic speed $... View answer 1 answers 2 votes 79 views Accepted answer 3 votes I assume that both pylons are composed of the same material. If you have a cylindrical pylon with height$h$and volume$V$then the radius can be calculated by$V = hA_{\text{base}} =h\pi r^2 \...

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According to my reference book on thermodynamics, the efficiency is given by: $$\eta = 1-\frac{1}{\varepsilon^{\varkappa-1}}.$$ The heat capacity ratio is given by $\varkappa$ and $\varepsilon$ is ...

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I can only try to give you an approximate answer. The principle is simple. We give rotational energy $E_{\text{rot}}$ into the system and we get axial force $F_{\text{ax}}$ times displacement $\Delta ... View answer 7 answers 2 votes 4k views 5 votes In general, we can distinguish four cases. Case: parallel --> If you take the curvature into account, the pillars cannot be treated as parallel. While I would guess that the error is pretty small on ... View answer 1 answers 0 votes 273 views 1 votes This task is not trivial at all. In order to get a crude estimate of the pressure distribution, we will assume inviscid flow. The flow is separated by a streamline in the middle (red line in the ... View answer 3 answers 0 votes 103 views 0 votes This is answering the second part of your question to get a mathematical relationship for the parameters that are involved. We write down the continuity equation in integral form.$\$\int_{V}\dfrac{\...