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A two level system can be represented on a Bloch sphere, as described in the class....
For a Mechanical Engineering System Dynamics class 3. A system is modeled with the following equations....
For a Mechanical Engineering System Dynamics class
3. A system is modeled with the following equations. * = y – 5x + d(t) y = 10f (t) – 30x The outputs are x(t) and y(t); the inputs are f(t) and d(t). a) b) c) From the two equations above, draw a complete block diagram for the model with X(s) at the rightmost position and F(s) at the leftmost position. All arrows must be shown clearly. Indicate the location of Y(s)...
For a causal LTI discrete-time system described by the difference equation:
For a causal LTI discrete-time system described by the difference equation: y[n] + y[n – 1] = x[n] a) Find the transfer function H(z).b) Find poles and zeros and then mark them on the z-plane (pole-zero plot). Is this system BIBO? c) Find its impulse response h[n]. d) Draw the z-domain block diagram (using the unit delay block z-1) of the discrete-time system. e) Find the output y[n] for input x[n] = 10 u[n] if all initial conditions are 0.
4. The two mass spring damper system below can be represented by the two differential equations...
4. The two mass spring damper system below can be represented by the two differential equations TIR1 Since the system is represented by two second-order differential equations, find a fourth-order state- space representation, that is y=Cz + Du where A e R1x4, BE Rx, CERix4, and D Rx1. Use the state vector Hint: first, solve the first equation for , then replace by 21, by z2, and r2 by z3 as defined by matrix-vector form.
2.2 Two-level system A particle in the box is described by the following wavefunction 1 1...
2.2 Two-level system A particle in the box is described by the following wavefunction 1 1 V(x, t) + V2 V2 = Um(x)e -i(Em/h) In other words, this state is a superposition of two modes: n-th, and m-th. A superposition that involves only two modes (not necessarily particle in the box modes, but any two modes) is called a "two-level system”. A more modern name for such a superposition is a "qubit”. a) Come up with an expression for the...
If you can draw a FBD as well 70. When an uncharged conducting sphere of radius...
If you can draw a FBD as well
70. When an uncharged conducting sphere of radius a is placed at the origin of an xyz coordinate system that lies in an initially uniform electric field E = E, Î, the resulting electric potential is V(x, y, z) = V, for points inside the sphere and E, az V(x, y, z) = V. – Eoz + (x2 + y2 + z2)3/2 for points outside the sphere, where V, is the (constant)...
The diagram below shows two negatively charged metal spheres, Sphere A and Sphere B. A positively...
The diagram below shows two negatively charged metal spheres,
Sphere A and Sphere B. A positively charged pith ball is placed at
the three locations shown. a)At each one of the three
locations, draw two field vectors, one for each of the two charged
spheres. Label each vector as EA and EB. For
each vector, draw the correct direction of the vector, and an
approximate relative length. These vectors represent the force that
the electric field exerts on the positive...
1.Three identical conducting spheres initially have the following charges: sphere A, 4Q; sphere B, −6Q; and...
1.Three identical conducting spheres initially have the following charges: sphere A, 4Q; sphere B, −6Q; and sphere C, 0. Spheres A and B are fixed in place, with a center-to- center separation that is much larger than the spheres. Two experiments are conducted. In experiment 1, sphere C is touched to sphere A and then (separately) to sphere B, and then it is removed. In experiment 2, starting with the same initial states, the procedure is reversed: Sphere C is...
Consider a two-tank system, where x, is the level of the first tank, and x2 is the level of the second tank. This dynamic system is described by the -xj-x2. The output to be Q4. following model: dt c...
Consider a two-tank system, where x, is the level of the first tank, and x2 is the level of the second tank. This dynamic system is described by the -xj-x2. The output to be Q4. following model: dt controlled is the level of the second tank. (a)Write down the state-space model in matrix form. Verify the 20% (b)Design a state feedback controller so that the closed-loop poles are 25% controllability of the system located at -3 and -4 (c) The...
The equations of motion for a mass-spring-damper system can be described by mE(t) + ci(t) +...
The equations of motion for a mass-spring-damper system can be described by mE(t) + ci(t) + k2(t) = F(t), where z(t) is the position of the mass, c is the damper coefficient, k is the spring constant, and F(t) is an external force applied to the mass as an input. If the system state vector is defined by 2(t) = lat) a(t)=F(t), y(t)=2(t), given below: x=Ax + Bu y=Cx + Du.
You have been asked to find the points on the sphere x2 + y2 + z2...
You have been asked to find the points on the sphere x2 + y2 + z2 = 36 that are closest to and farthest from the point (1, 2, 2). Then which of the following is incorrect from the following: Select one: A. The point on the sphere farthest to the point (1,2,2) is (-2,-4,-4) B. The point on the sphere closest to the point (1,2,2) is (2, 4,4) C. The solutions to the question can be found by solving...
For a Mechanical Engineering System Dynamics class
3. A system is modeled with the following equations. * = y – 5x + d(t) y = 10f (t) – 30x The outputs are x(t) and y(t); the inputs are f(t) and d(t). a) b) c) From the two equations above, draw a complete block diagram for the model with X(s) at the rightmost position and F(s) at the leftmost position. All arrows must be shown clearly. Indicate the location of Y(s)...
4. The two mass spring damper system below can be represented by the two differential equations TIR1 Since the system is represented by two second-order differential equations, find a fourth-order state- space representation, that is y=Cz + Du where A e R1x4, BE Rx, CERix4, and D Rx1. Use the state vector Hint: first, solve the first equation for , then replace by 21, by z2, and r2 by z3 as defined by matrix-vector form.
2.2 Two-level system A particle in the box is described by the following wavefunction 1 1 V(x, t) + V2 V2 = Um(x)e -i(Em/h) In other words, this state is a superposition of two modes: n-th, and m-th. A superposition that involves only two modes (not necessarily particle in the box modes, but any two modes) is called a "two-level system”. A more modern name for such a superposition is a "qubit”. a) Come up with an expression for the...
If you can draw a FBD as well
70. When an uncharged conducting sphere of radius a is placed at the origin of an xyz coordinate system that lies in an initially uniform electric field E = E, Î, the resulting electric potential is V(x, y, z) = V, for points inside the sphere and E, az V(x, y, z) = V. – Eoz + (x2 + y2 + z2)3/2 for points outside the sphere, where V, is the (constant)...
The diagram below shows two negatively charged metal spheres,
Sphere A and Sphere B. A positively charged pith ball is placed at
the three locations shown. a)At each one of the three
locations, draw two field vectors, one for each of the two charged
spheres. Label each vector as EA and EB. For
each vector, draw the correct direction of the vector, and an
approximate relative length. These vectors represent the force that
the electric field exerts on the positive...
Consider a two-tank system, where x, is the level of the first tank, and x2 is the level of the second tank. This dynamic system is described by the -xj-x2. The output to be Q4. following model: dt controlled is the level of the second tank. (a)Write down the state-space model in matrix form. Verify the 20% (b)Design a state feedback controller so that the closed-loop poles are 25% controllability of the system located at -3 and -4 (c) The...
The equations of motion for a mass-spring-damper system can be described by mE(t) + ci(t) + k2(t) = F(t), where z(t) is the position of the mass, c is the damper coefficient, k is the spring constant, and F(t) is an external force applied to the mass as an input. If the system state vector is defined by 2(t) = lat) a(t)=F(t), y(t)=2(t), given below: x=Ax + Bu y=Cx + Du.
You have been asked to find the points on the sphere x2 + y2 + z2 = 36 that are closest to and farthest from the point (1, 2, 2). Then which of the following is incorrect from the following: Select one: A. The point on the sphere farthest to the point (1,2,2) is (-2,-4,-4) B. The point on the sphere closest to the point (1,2,2) is (2, 4,4) C. The solutions to the question can be found by solving...
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