Given the System described by the differential equation below: D^2 y(t) + 3 Dy(t) + 2y(t)...
Given the System described by the differential equation below:
D^2 y(t) + 3 Dy(t) + 2y(t) = x(t) where D=d/dt and D^2 is the second derivative
1) find its Transfer Function H(s) (assume all initial conditions are zero)
2) use the first procedural way of getting A, B, C, D from H(s) to find the corresponding state space representations . Then do the reverse step of finding H(s) from the A, B, C, D representation just found (i.e. check that H(s) obtained from the state space representation matches the one initially used)
3) repeat the second part above using the second procedural way shown in notes
4) Write the expression for y(t) total response from the A, B, C, D (write the general form solution leaving it in terms A, B, C, D, x(t) ).
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Given the System described by the differential equation
below:
D^2 y(t) + 3 Dy(t) + 2y(t)...
Consider the linear system given by the following differential equation y(4) + 3y(3) + 2y +...
Consider the linear system given by the following differential equation y(4) + 3y(3) + 2y + 3y + 2y = ů – u where u = r(t) is the input and y is the output. Do not use MATLAB! a) Find the transfer function of the system (assume zero initial conditions)? b) Is this system stable? Show your work to justify your claim. Note: y(4) is the fourth derivative of y. Hint: Use the Routh-Hurwitz stability criterion! c) Write the...
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slove the system eqution: d^3y(t)/dt^3 - 2 d^2y(t)/dt^2 - 5 dy(t)/dt +6 y(t) = 2 d^2u(t)/dt^2 +du(t)/dt +u(t) A) compute the transfer function Y(s)/U(s)? B)Find inverse Laplace for y(t) and x(t)? C) find the final value of the system? D)find the initial value of the system? Please solve clearly with steps.
Calculate the first AND second derivative dy/dx and d^2y/dx^2 for the curve given by: r(t) =...
Calculate the first AND second derivative dy/dx and d^2y/dx^2
for the curve given by:
r(t) = t-t, y(t) = 3t - t
dy(D), 5) Consider a causal LTI system S described by the following differential equation: 2 +...
dy(D), 5) Consider a causal LTI system S described by the following differential equation: 2 + 3y(t) = x(t). Draw a block digram representation for S. Then, convert this differential equation into an integral equation, and draw a corresponding block diagram representation. dt
Find the particular solution such that y=0 when t=0 of the differential equation: (dy/dt) - 2y...
Find the particular solution such that y=0 when t=0 of the differential equation: (dy/dt) - 2y = t
3. Consider a linear time invariant system described by the differential equation dy(t) dt RCww +...
3. Consider a linear time invariant system described by the differential equation dy(t) dt RCww + y(t)-x(t) where yt) is the system's output, x(t) ?s the system's input, and R and C are both positive real constants. a) Determine both the magnitude and phase of the system's frequency response. b) Determine the frequency spectrum of c) Determine the spectrum of the system's output, y(r), when d) Determine the system's steady state output response x()-1+cos(t) xu)+cost)
dt - Solve the following equation for y(t) using Fourier Transforms. dy(t) ? +2y(t) = {...
dt - Solve the following equation for y(t) using Fourier Transforms. dy(t) ? +2y(t) = { 'h(t) where h(t) is the Heaviside function: (0,t=0 h(t)= | 1,20 Note: the solution satisfies ly(t) >0 as t →+00.
d’y(t) 4x(t) = + 3 dy(t) - +2y(t) dt2 +34 dt For the system presented in...
d’y(t) 4x(t) = + 3 dy(t) - +2y(t) dt2 +34 dt For the system presented in Part 2, sketch its input/output block diagram including any feedback loops. Be explicit in whether you are presenting this figure in a time- domain or s-domain representation.
Consider an LTI system: dy(t) +2y(t) = 3x(t) and H(jk 12) = dt 3 2+jk 12...
Consider an LTI system: dy(t) +2y(t) = 3x(t) and H(jk 12) = dt 3 2+jk 12 If the output to the system is, y(t) = 1 + cos(2t), what was the input?
2 Y, Y(t) 2 dY 5. For the system dt - 2. a) Write the general...
2 Y, Y(t) 2 dY 5. For the system dt - 2. a) Write the general solution. b) State if the origin is a spiral sink, or a source, or a center. c) Write the natural period and the natural frequency of the solutions. d) Do the solutions go clockwise or anti clockwise around the origin? (0) e) Write the particular solution that corresponds to ly(0) =
Consider the linear system given by the following differential equation y(4) + 3y(3) + 2y + 3y + 2y = ů – u where u = r(t) is the input and y is the output. Do not use MATLAB! a) Find the transfer function of the system (assume zero initial conditions)? b) Is this system stable? Show your work to justify your claim. Note: y(4) is the fourth derivative of y. Hint: Use the Routh-Hurwitz stability criterion! c) Write the...
Calculate the first AND second derivative dy/dx and d^2y/dx^2
for the curve given by:
r(t) = t-t, y(t) = 3t - t
dy(D), 5) Consider a causal LTI system S described by the following differential equation: 2 + 3y(t) = x(t). Draw a block digram representation for S. Then, convert this differential equation into an integral equation, and draw a corresponding block diagram representation. dt
3. Consider a linear time invariant system described by the differential equation dy(t) dt RCww + y(t)-x(t) where yt) is the system's output, x(t) ?s the system's input, and R and C are both positive real constants. a) Determine both the magnitude and phase of the system's frequency response. b) Determine the frequency spectrum of c) Determine the spectrum of the system's output, y(r), when d) Determine the system's steady state output response x()-1+cos(t) xu)+cost)
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Consider an LTI system: dy(t) +2y(t) = 3x(t) and H(jk 12) = dt 3 2+jk 12 If the output to the system is, y(t) = 1 + cos(2t), what was the input?
2 Y, Y(t) 2 dY 5. For the system dt - 2. a) Write the general solution. b) State if the origin is a spiral sink, or a source, or a center. c) Write the natural period and the natural frequency of the solutions. d) Do the solutions go clockwise or anti clockwise around the origin? (0) e) Write the particular solution that corresponds to ly(0) =
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