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1. the function f(t) illustrated in the following figure, and defined as shown on the right...
11. (10 points) Let f(t) be a 27-periodic function defined by f(t) = -{ 2 if...
11. (10 points) Let f(t) be a 27-periodic function defined by f(t) = -{ 2 if – <t<0, -2 if 0 <t<, f(t + 2) = f(t). a) Find the Fourier series of f(t). b) What is the sum of the Fourier series of f at t = /2.
2. Given 12 f(t)= ={ Ost<3 t23 (a) Write f(t) in one line using the unit...
2. Given 12 f(t)= ={ Ost<3 t23 (a) Write f(t) in one line using the unit step function (Heaviside function). 5 points 10 points (b) Find L{f(t)}, either by using the definition of the Laplace transform or by finding the Laplace transform of your answer to part (a).
please answer both questions 3. A function f(t) defined on an interval 0 <t<L is given....
please answer both questions
3. A function f(t) defined on an interval 0 <t<L is given. Find the Fourier cosine and sine series of f. f() = 6(1-1),0 <t< 4. Find the steady state periodic solution, *xp(t) of the following differential equation. *" + 5x = F(t), where FC) is the function of period 2nt such that F(t) = 18 if 0 << < 1 and F(t) = -18 if t <t <200.
34.3 Let f be defined as follows: f(t) = 0 for t < 0; f(t) =...
34.3 Let f be defined as follows: f(t) = 0 for t < 0; f(t) = t for 0 <t < 1; f(t) = 4 for t > 1. (a) Determine the function F(x) = $* f(t) dt. (b) Sketch F. Where is F continuous? (c) Where is F differentiable? Calculate F' at the points of differentiability.
х 0<I< 3. The tent function is defined by T(x) = 1 - < x <...
х 0<I< 3. The tent function is defined by T(x) = 1 - < x < 1 2 otherwise (a) Express T(2) in terms of the Heaviside function. (b) Find the Laplace transform of T(x). (c) Solve the differential equation y" – y=T(x), y(0) = y'(0) = 0
Find the Laplace transform of the given function. (Enter your answer in terms of s.) f(t)...
Find the Laplace transform of the given function. (Enter your answer in terms of s.) f(t) = 3, 0, Ost < Ist < 00 L{f(t)} =
Evaluate the piecewise-defined function for the given values. f(x) = 4x for x 20 - 4x...
Evaluate the piecewise-defined function for the given values. f(x) = 4x for x 20 - 4x for x < 0 Find f(1), f(2), f(-1), and f(-2). f(1) f(2) f(-1) = f(-2) =
QUESTION 7 Find the Laplace transform of the function f(t) = t, 0 <t<1 1, t>1...
QUESTION 7 Find the Laplace transform of the function f(t) = t, 0 <t<1 1, t>1 S e S s2 - e-s S 1 e-(s-1) S 32 S e OD. 1- $2 - e $2
The Laplace transform of the plecewise continuous function f(t) = S4, 0<t<3 12, t> 3 Is...
The Laplace transform of the plecewise continuous function f(t) = S4, 0<t<3 12, t> 3 Is given by [{f} = { (3 – e-"), o>0. None of them 1 [{f} = (1 – 2e-4), 8>0. 0 [11] = (1 – 3e-4), 0> 0. ° L{f} = { (2–e=4), o>0.
P3. In the circuit shown, let DUO 0, -00<t<0 v(t) = { 1, Ost<10s at (10,...
P3. In the circuit shown, let DUO 0, -00<t<0 v(t) = { 1, Ost<10s at (10, 1055t<00 (a) Find the energy stored in the capacitor as a function of t, for 0 st 50. (b) Find the energy delivered by the source as a function of t, for 0 stsoo. va) 0.1F 322 Figure P4.7
11. (10 points) Let f(t) be a 27-periodic function defined by f(t) = -{ 2 if – <t<0, -2 if 0 <t<, f(t + 2) = f(t). a) Find the Fourier series of f(t). b) What is the sum of the Fourier series of f at t = /2.
2. Given 12 f(t)= ={ Ost<3 t23 (a) Write f(t) in one line using the unit step function (Heaviside function). 5 points 10 points (b) Find L{f(t)}, either by using the definition of the Laplace transform or by finding the Laplace transform of your answer to part (a).
please answer both questions
3. A function f(t) defined on an interval 0 <t<L is given. Find the Fourier cosine and sine series of f. f() = 6(1-1),0 <t< 4. Find the steady state periodic solution, *xp(t) of the following differential equation. *" + 5x = F(t), where FC) is the function of period 2nt such that F(t) = 18 if 0 << < 1 and F(t) = -18 if t <t <200.
34.3 Let f be defined as follows: f(t) = 0 for t < 0; f(t) = t for 0 <t < 1; f(t) = 4 for t > 1. (a) Determine the function F(x) = $* f(t) dt. (b) Sketch F. Where is F continuous? (c) Where is F differentiable? Calculate F' at the points of differentiability.
х 0<I< 3. The tent function is defined by T(x) = 1 - < x < 1 2 otherwise (a) Express T(2) in terms of the Heaviside function. (b) Find the Laplace transform of T(x). (c) Solve the differential equation y" – y=T(x), y(0) = y'(0) = 0
Find the Laplace transform of the given function. (Enter your answer in terms of s.) f(t) = 3, 0, Ost < Ist < 00 L{f(t)} =
Evaluate the piecewise-defined function for the given values. f(x) = 4x for x 20 - 4x for x < 0 Find f(1), f(2), f(-1), and f(-2). f(1) f(2) f(-1) = f(-2) =
QUESTION 7 Find the Laplace transform of the function f(t) = t, 0 <t<1 1, t>1 S e S s2 - e-s S 1 e-(s-1) S 32 S e OD. 1- $2 - e $2
The Laplace transform of the plecewise continuous function f(t) = S4, 0<t<3 12, t> 3 Is given by [{f} = { (3 – e-"), o>0. None of them 1 [{f} = (1 – 2e-4), 8>0. 0 [11] = (1 – 3e-4), 0> 0. ° L{f} = { (2–e=4), o>0.
P3. In the circuit shown, let DUO 0, -00<t<0 v(t) = { 1, Ost<10s at (10, 1055t<00 (a) Find the energy stored in the capacitor as a function of t, for 0 st 50. (b) Find the energy delivered by the source as a function of t, for 0 stsoo. va) 0.1F 322 Figure P4.7
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