4

No, positive acceleration, alone, does not need to imply positive velocity. Another term for "acceleration in the opposite direction of the velocity" is just "deceleration". The negative value is being rejected based on physical context. That is, it is being rejected based on the fact you are starting from rest along with the fact that ...


3

Since you will be using a guide, then my thoughts are the following. Assume at some point the rod forms an angle $\phi$. General Idea Since you are pushing up the platform the downward component of the force is equal to the reaction on the pivot below the platform $R_{1y}$. this will create a horizontal component on the rod which will need to satisfy the ...


3

Most acoustic vibrations of air more or less confined to a given geometry can be explained by two basic models. One is the one-dimensional treatment of the air in a tube, and the other is the lumped-parameter treatment of the air within a volume that has a small hole in its side. The former is called a quarter-wave or half-wave tube, depending on the nature ...


3

The frequency of the sound you're hearing is related to the changing resonant frequency of your bottle based on the frequency/velocity relationship of sound waves v=f*λ Velocity (v) is the speed of sound in air which is nearly constant, typically 343 m/s. The length of the air column in your bottle is the wavelength (λ) of the resonant frequency. So as the ...


3

Given the geometry of the object, the center of gravity is very close to the surface between the cylinder and the cone. More specifically the distance between the center of gravity and the base of the cone is $\frac{1}{4}r$. Basically what you need to prove is that the angle of the cone $ \phi$ is such, so that when the object is tilted the weight crosses ...


2

I agree totally with Jonathan R Swift's answer but I will try to give a insight as to why it is not appropriate to use a shock absorber. The main issue is that the excitation frequency of the vibration is not constant. The vibrations frequency will change depending on how fast the car will travel and on the roughness of the road. All things being equal if ...


2

Usually if you can get rid of extra vibration of car seat and be satisfied with the vibration of the car itself you should be happy. For examplev the instrument panel of an airplane is the absolute most critical interface between the pilot and the plane. it is directly mounted on the frame. They would have mounted it on a shock absorber base if it would help....


2

The problem is with $$v_C = v_A + \Omega_{AC} \times r_{AC} + v_{rel}$$ More specifically, you are getting confused with what it means to have a different coordinate system. In your image you have $XY$ (which is at an angle) and $\color{red}{XY}$ which is horizontal and vertical. That means that you have $\vec{i}$ and $\color{red}{\vec{i}}$ respectively. So ...


2

Input signal: ±U V. Scaled output signal: ±1 V. Required gain: $ \frac 1 U $. Figure 1. Possible solutions. If U > 1 then a simple potential divider may suffice. $ V_{OUT} = \frac {R_2}{R_1+R_2} $. Bear in mind that whatever follows this circuit may load it somewhat so keep the parallel combination value of R1 || R2 < 10% of the value of the ...


2

The normal and the tangential axis at any moment describe a trajectory in a plane, (even in the generic 3d motion). I.e. if you sum all the forces and obtain a resultant force acting on the particle, then the projection of the resultant force: on the tangential axis will be responsible for the increase/decrease of the velocity magnitude. on the normal axis ...


2

You should look at Ackerman Steering. You don't really need to modify anything apart from the length of the rack. What you need to modify are the steering arms and ties. A simplified version is shown in the image below. Figure 1: Ackerman steering geometry (source: Wikipedia The easiest way, is use a parametric design software (Inventor, Solidworks etc) and ...


2

I suggest using the relationship below to derive the equations you are looking for. $F = ma$ $W = mg$ $D = \dfrac{C_d\rho V^2A}{2}$ $C_d$ = Drag Coefficient (Shape dependent) $\rho$ = Atmospheric Density The terminal velocity is reached when $W = D$, $mg = \dfrac{C_d\rho V^2A}{2}$, thus $V_t = \sqrt{\dfrac{2mg}{C_d \rho A}}$ Note, at this stage, $a = \dfrac{...


1

As PeteW mentioned you can differentiate both sides of the equation with respect to t, and then solve for $\dot\theta(t)$. If I done correct the calculations, you'll end up with $$\dot\theta(t) = -\frac{X'(t)}{a(\theta(t)) + b(\theta(t))}$$ where: $a(\theta(t))= -H_{p} \cos(\theta(t))+ \frac{1}{2} W_{P} \sin(\theta(t))-L_{rod} \arcsin\left(\frac{H_T-H_{p} \...


1

Using the following coordinates: i.e.: using pulley one (top left as the reference point: $x_1$ the distance of mass 1 from pulley 1 $x_2$ the distance of mass 2 from pulley 1 $P_2$ the distance of pulley 2 from pulley 1 $P_3$ the distance of pulley 3 from pulley 1 then the equations are the following: for rope wrapped around pulley 1 $$L_1 = x_1 + P_2$$...


1

First of all, the two methods you suggested (buying pad materials and spring+damper) are not necessarily different. Usually the different pad materials that can be bought, (mainly) modify the spring constant in the structure. Additionally, although there are methods of targeting specific frequencies, in most cases they are not very useful. The reason, is ...


1

Im going to step out of the comment section as it is fairly limited. The quickest answer to the question: Is it possible to somehow form a transient process (with given properties) if the steady state is not known in advance, but it is known that in the steady state f(x,t)=0? Given the proposed conditions is simple: no. And the explanation boils down to ...


1

Find the transfer function $\delta_r(t)\to \psi (t)$ and $\delta _r(t)\to \beta (t)$. Divide the first transfer function by the second to get the transfer function $\beta (t)\to \psi (t)$. These calculations can be tedious. I used Mathematica to get the following result. ssm = StateSpaceModel[{p'[t] == -11.450 p[t] + 2.7185 r[t] - 19.4399 \[Beta][t] + ...


1

Why dont you construct a state-space model from the given equations (which happen to be in the appropriate form) and either continue using the state space model or convert it to a transfer function in matlab. A continuous-time state-space model looks like this: $$\dot{x} = Ax + Bu$$ $$y = Cx+Du$$ Where $x$ and $u$ are vectors and $A$ and $B$ matrices. $$\...


1

Again your basic formula is just fine. $\tau=I_o \cdot \alpha$,. Therefore $$ \alpha = \frac{\tau}{I_o}$$ The reason why you are getting such a high acceleration is due to the very high torque $\tau$ with respect to the reported mass moment of inertia and radius. I would crosscheck the values regarding the mass moment of inertia because given the radius and ...


1

The CG is found by assuming the mass of the cone as 1/3m and the cylinder m, then $$ \bar{X}= \frac{2r*m+5r*m/3}{4/3m} =r*11/4 $$ The cone side length (like the sharp tip of a pencil) is $5r$, the side of a 3,4,5 triangle, and the interior half tip angle is 36.87 degrees. The CG is $5.25r$ from the tip of the cone and at rotation to rest on the side of the ...


1

yes, a disk rotating about its center axis with moment of inertia I and angular velocity $\omega$ has angular momentum $L$: $$L = I \cdot \omega$$ it is as simple as that.


1

Creating an output from 2 inputs won't have more precision; it will have 2 sources of error. If you are trying to control relative humidity, then using that as your control variable only makes sense.


1

You are right in that the you the relative humidity will be quicker and easier to control. The question is whether that matter for your problem. Absolute humidity is the measure of water vapor (moisture) in the air, regardless of temperature. It is expressed as grams of moisture per cubic meter of air ($g/m^3$). Relative humidity is the ratio of water vapor ...


1

The equation of motion after the impulse is $$m\ddot x + c\dot x + kx = 0$$ with initial conditions $$x = 0, \dot x = \dot x_0 \text{ when } t = 0.$$ You have found the frequency and damping ratio already, so you can rewrite the EOM as $$m(\ddot x + \beta \omega\dot x + \omega^2 x) = 0$$ where you know $\beta$ and $\omega$. Scale your measured results to ...


1

Your question is related to rotating frames of reference and the Coriolis Force. As a passenger you are going to be experiencing a lateral force which will be greater the the faster you are travelling. The magnitude of the acceleration you'd feel would be $$a_{coriolis} = -2\omega\times v_{train} $$ and the force would be : $$F_{coriolis}= -2\cdot m\cdot \...


1

I would argue that there are only 3 degrees of freedom in this system. Those can be the following (you can define others also): The idea behind the DOF is a motion that is required to describe the motion of the system. The pulleys at the top of the image do not translate (even if you want to calculate their rotation you can calculate it through the ...


1

A pure torque applied to a rigid body doesn't have a point of application. But if the torque is the result of some forces to that body more likely there will be a force F passing through the Center of the mass of the body and a torque applied to the body. note how the resultant of the forces have simplified to torque and a force F applied at the CG of the ...


1

If im not mistaken the angle is increasing when the door is opening. That is defined as positive angular displacement. On the other hand if you see the moments that are acting in the door they appear to be directed towards clouding the door. Thus the -sign in the equation.


1

The problem is complicated by the fact that the function f(t) and the point at which its minimum/maximum x∗ is located, generally speaking, are not known to us. So if I understand it correctly: $f(t)$ is a unknown function, of which your controlled system should approach either the maximum or the minimum value $f(t)$ has over $t$. If I look at your system ...


1

Maybe something like this: Step 1: By the previous answer, the coordinate $X_A = X_A(t)$ and the angle $\theta = \theta(t)$ are connected by the equation $$\big(\,X_A + l \cos(\theta + \varphi_0) - c\,\big)^2 \, + \, \big(\,sX_A + l \sin(\theta + \varphi_0) + b\,\big)^2 \, = \, r^2$$ Knowing $X_A$, plug it in the equation and solve for $\theta$. Step 2: ...


Only top voted, non community-wiki answers of a minimum length are eligible