Let f (t) = { 7 0 ≤ t ≤ 2π cos(5t) 2π < t ≤ ...

Let

f (t) =

{	7	0 ≤ t ≤ 2π
	cos(5t)	2π < t ≤ 4π
	e^3(t−4π)	t > 4π

(a)	f (t) can be written in the form g₁(t) + g₂(t)U(t − 2π) + g₃(t)U(t − 4π) where U(t) is the Heaviside function. Enter the functions g₁(t), g₂(t), and g₃(t), into the answer box below (in that order), separated with commas.

(b)	Compute the Laplace transform of f (t).

Solutions

Expert Solution

Please UPVOTE if this answer helps you understand better.

Solution:-

Please UPVOTE if this answer helps you understand better.

milcah answered 1 year ago

Next > < Previous

Related Solutions

If u(t) = < sin(5t), cos(5t), t > and v(t) = < t, cos(5t), sin(5t) >,...

If u(t) = < sin(5t), cos(5t), t > and v(t) = < t, cos(5t), sin(5t) >, use the formula below to find the given derivative. d/dt[ u(t) * v(t)] = u'(t) * v(t) + u(t)* v'(t) d/dt [ u(t) x v(t)] = ?

Let f be a differentiable function on the interval [0, 2π] with derivative f' . Show...

Let f be a differentiable function on the interval [0, 2π] with derivative f' . Show that there exists a point c ∈ (0, 2π) such that cos(c)f(c) + sin(c)f'(c) = 2 sin(c).

Consider the function on the interval (0, 2π). f(x) = sin(x) cos(x) + 2 (a) Find...

Consider the function on the interval (0, 2π). f(x) = sin(x) cos(x) + 2 (a) Find the open interval(s) on which the function is increasing or decreasing. (Enter your answers using interval notation.) increasing ( ) decreasing ( ) (b) Apply the First Derivative Test to identify all relative extrema. relative maxima (x, y) = (smaller x-value) (x, y) = ( ) (larger x-value) relative minima (x, y) = (smaller x-value) (x, y) = ...

Consider the function on the interval (0, 2π). f(x) = sin(x)/ 2 + (cos(x))^2 (a) Find...

Consider the function on the interval (0, 2π). f(x) = sin(x)/ 2 + (cos(x))^2 (a) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.) increasing decreasing (b) Apply the First Derivative Test to identify the relative extrema. relative maximum (x, y) = relative minimum (x, y) =

7. Find the solution of the following PDEs: ut−16uxx =0 u(0,t) = u(2π,t) = 0 u(x,...

7. Find the solution of the following PDEs: ut−16uxx =0 u(0,t) = u(2π,t) = 0 u(x, 0) = π/2 − |x − π/2|

Find the solution of y′′+5y′=100sin(5t)+250cos(5t) with y(0)=7 and y′(0)=3.

1.The domain of r(t)=〈sin(t),cos(t),ln(t+1)〉 is Select one: a. (−∞,−1] b. (π,2π) c. (−∞,−2] d. (−π,2π) e....

1.The domain of r(t)=〈sin(t),cos(t),ln(t+1)〉 is Select one: a. (−∞,−1] b. (π,2π) c. (−∞,−2] d. (−π,2π) e. ℝ f. (−1,∞) 2. The limt→πr(t) where r(t)=〈t2,et,cos(t)〉 is Select one: a. 〈π2,eπ,−1〉 b. undefined c. 〈π2,eπ,1〉 d. π2+eπ e. 〈π2,eπ,0〉 3.Let v(t)=〈2t,4t,t2〉. Then the length of v′(t) is Select one: a. 20‾‾‾√+2t b. 20+4t2 c. 20+2t‾‾‾‾‾‾‾√ d. 20+4t2‾‾‾‾‾‾‾‾√ e. 6+2t‾‾‾‾‾‾√ f. 1 4. The curvature of a circle centred at the origin with radius 1/3 is Select one: a. 1 b. 1/3 c....

For the given function f(x) = cos(x), let x0 = 0, x1 = 0.25, and x2...

For the given function f(x) = cos(x), let x0 = 0, x1 = 0.25, and x2 = 0.5. Construct interpolation polynomials of degree at most one and at most two to approximate f(0.15)

A periodic function f(t) of period T=2π is defined as f(t)=2t ^2 over the period -π<t<π...

A periodic function f(t) of period T=2π is defined as f(t)=2t ^2 over the period -π<t<π i) Sketch the function over the interval -3π<t<3π ii) Find the circular frequency w(omega) and the symmetry of the function (odd, even or neither). iii) Determine the trigonometric Fourier coefficients for the function f(t) iv) Write down its Fourier series for n=0, 1, 2, 3 where n is the harmonic number. v) Determine the Fourier series for the function g(t)=2t^ 2 -1 over the...

Plot the solution of the equation 6ẏ + y = f(t) if f (t) = 0 for t + 0 and f(t) = 15 f

Plot the solution of the equation6ẏ + y = f(t) if f (t) = 0 for t + 0 and f(t) = 15 for t ≥ 0. The initial condition is y(0) = 7.

Subjects