1. Find the Laplace transforms of the following functions: (a) f(t) = e-4' cos(2t)8(t-3) (b) f(t) = (t2 + 2) u(t – 2), where u is the unit step function

Q: Laplace transforms

A:

Q: Find the Fourier transform of the function f(t) = e-2. 2. ii. Using Fourier transforms prop erties…

A: The Fourier transform of the function is represented as , it is defined as , where . Since the…

Q: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

A: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

Q: Q.5A/Find Laplace Transform of the following functions 1.f(t) = 6e-6t + +5t3-9 2./(t) = (42marke)…

A:

Q: 2C

A:

Q: Q2 \ Determine the Laplace transforms of the following function: t | e-4tt sin? 3t dt L

A:

Q: 1. Find the Laplace transforms of the following functions using the table of Laplace transforms and…

A: Solution :-    The given functions are                 (a)   f(t) =  4t2 - 5sin(3t)…

Q: 4. Find the Laplace transform of the following functions. a) f(t) = t sint cos t. b) f(t) = t°c#6 (t…

A: By using the formua sin2x =sin x cos x simplify the given function f(t)

Q: Compute the Laplace transforms of the following functions; i. f(t) = 6e-5t +e3t + 5tª – 10 ii. g(t)…

A:

Q: 2.x²y"+xy'–3y= 0,x>0

A:

Q: Use Theorem 7.4.1. THEOREM 7.4.1 Derivatives of Transforms If F(s) = L{f(t)} and n = 1, 2, 3, . . .…

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: Find the Laplace transforms of the following functions using the definition L{f(t)} =fe-st f(t)dt. =

A:

Q: a) Consider the following function UTM UT Cos t, cos 2t, 0 T. UTM ii. Hence, find its Laplace…

A: The given problem is to express the given function in terms of unit step function and also find the…

Q: . Find the laplace transform of the 1VP: y" - 4y = et + t, y = y'(0) = y" (0) = 0

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: f(t) = [1– u2m(t)](2 sin t – sin 2t) U2n

A: Some of the properties of Laplace transformation Lsinat=as2+a2Luc(t)=e-cssLuc(t)g(t)=e-csL[g(t+c)]

Q: Find the Laplace Transform of (i) e3(2cos 5t - 3sin 5t) (ii) e2tcos² t 4t (iii) e**sin 2t cos t

A:

Q: 2. Determine the Laplace transform of the given function a) f(t) = e³¹t4 b) f(t

A: Laplace transform

Q: 1. Find the Laplace transforms for the given f(t). (h) f(t) = 3 sinh At (i) f(t) = e-2t cos 3t (j)…

A: Solution is given below:-

Q: Let F(s) be the Laplace transform of f(t) = cos (k(t – 7)] e" sin(37)dr, where k is a positive…

A:

Q: Apply Fourier transform, jw F(w) = F₁ (w) + F₂ (w)...... equation 2 |F₁(t) = −8(t + 2) +…

A:

Q: Use the formula £{t" f(t)} (s) = ( – 1)" – (L{f}(s)) to help determine the following the…

A: We will use formula for derivative of u/v and given formula to solve as follows

Q: (b) Given f(t) = sinh(-4t)U(t – )and g(t) = sinh(-4t) * U(t – ) %3D where U(t - a) is the unit step…

A: The solution is given as

Q: Find the Laplace Transform of the following functions: 1. f(t) = (2e−4t + sin t)² 2. f(t) = 4t cosh…

A: To find: Laplace transform of the following function:-               1. ft=2e-4t+sint2…

Q: 3. Find the laplace transforms of f(t) = ¹e²t sin(2t) 2t 4

A:

Q: (b) Sketch the following function. Write down its equation in unit step function and find its…

A:

Q: 2) Sketch the graph of the following s functions and find the Laplace transfo a) f1(t) = }4 – t, (o,…

A: Given,      (a)    f1(t)=t0≤t<24-t2≤t<40t≥4      (b)    f2(t)=00≤t<1t1≤t<21t≥2

Q: 1. The Laplace transform of the function y(t) = t5 is a. 20/s5 b. 1/(s-5)6 c. 120/s6 2. The Laplace…

A: Note: Hi! Thank you for the question, As per the honour code, we are allowed to answer three…

Q: 2. Determine the Laplace transform of the given function. a) f(t) = e³¹t4 c) f(t) = est sin(3t) e)…

A: Recall the formula of Laplace transform: For any non-negative integers L{tn}=n!sn+1 .The property of…

Q: Find the Laplace transforms of f(t) = e(3t-7) cos3(6t).

A:

Q: Calculate the Laplace transform of: a. f(t) = t sinh (at) b. f(t)=1²e-t c. f(0) = √i

A:

Q: 4. Find the Laplace transform of the following functions. a) f(t)=t(sinh t + cosh t)² b) f(t) =…

A: The given functions are ft=tsinht+cosht2 and ft=t2e-4tδt-1   The Laplace transform of sinht is ℒsinh…