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Consider the first-order linear system
x· (t) = A [x (t) - u (t)]
with A < 0. Note that tyhe system is stable, the time constant is τc = 1/(-A), and the steady-sate gain from u to x is 1. Suppose the input (for t ≥ 0) is a ramp input, that is
u(t) = βt
(where β is a known constant) starting with an initial condition x(0) = x0. Show that the solution for t ≥ 0 is
x(t)= β (t - τc)+(x0 + βτc)eAt
Make an accurate sketch of u(t) and x(t) (versus t) on the same graph, for x0 = 0, β = 3 and A = 0.5.
Write each number given in as a decimal numeral.
find the equations of the bisectors of the angles between the lines 4x3y-120 and
Find the average velocity for the time period beginning when t=3 and lasting
draw a triangle PQR such that angle Q=115degree.Draw its altitudes PL and QM to the lines containing opposite sides .let the two altitudes meet at H .Join RH meeting PQ at N.
Out of class activities that I could employ to make students aware of congruent objects could be: How does running and playing soccer make students aware of congruent objects?
Suppose that f(x; y) is a function of two variables with continuous first and second partial derivatives whose quadratic approximation about the point (2; 1) is Q(x; y) = 4 8(y 1) (x 2)2 + 8(x 2)(y 1):
Find the largest possible values for the base length and height, to the nearest foot, as well as the volume of each pyramid, in scientific notation to 3 decimal places.
Consider the following linear mapping from C[-pi,pi] into itself: L(f)=integral from -pi to pi of G(x),h(y),f(y)dy for any function f(x) in C[-pi,pi].
A heavy rope, 30 ft long, weighs 0.6 lb/ft and hangs over the edge of a building 70 ft high. How much work W is done in pulling half the rope to the top of the building?
bills train leaves at 806 am and accelerates at the rate of 2meters per second per second. bill who can run 5 meters
If the periphelion of mars is 128.5 million miles, what is the aphelion? Write an equation for the orbit of mars about the sun.
Define a topological space X with a subspace A. Find and describe a pair of sets that are a separation of A in X
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