Multiplication by Powers of t 1. f(t) = 4t sin 2t 2. f(t) = 4t^3 sint...

Multiplication by Powers of t

1. f(t) = 4t sin 2t

2. f(t) = 4t^3 sint t

3. f(t) = t^3 cos t

Expert Solution

Applied laplace transform to given function by using "Multiplication by powers of t " method.

If you any dought please let me know in the comment section below and they will be clarified.

Please rate the question and give feedback...thank you.

Colby Messinger answered 1 month ago

If u(t) = < sin(8t), cos(4t), t > and v(t) = < t, cos(4t), sin(8t) >,...

If u(t) = < sin(8t), cos(4t), t > and v(t) = < t, cos(4t), sin(8t) >, 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)] = <.______ , _________ , _______>

For this parametrized curve: x = e^(2t) sin t , y = cos(4t) find tangent line...

For this parametrized curve: x = e^(2t) sin t , y = cos(4t) find tangent line to curve when t=1

How do I graph this step function? f(t) = -3(2t-3)H(t-2) + (2t-1)H(t-1) Please show step by...

How do I graph this step function? f(t) = -3(2t-3)H(t-2) + (2t-1)H(t-1) Please show step by step. How is it the same graph as f(t) = H(t-1)-3H(t-2)+H(t-1)*2(t-1)-H(t-2)*6(t-2)? Please show why as well.

Consider the helix r(t)=(cos(2t),sin(2t),−3t)r(t)=(cos(2t),sin(2t),−3t). Compute, at t=π/6 A. The unit tangent vector T=T= ( , ,...

Consider the helix r(t)=(cos(2t),sin(2t),−3t)r(t)=(cos(2t),sin(2t),−3t). Compute, at t=π/6 A. The unit tangent vector T=T= ( , , ) B. The unit normal vector N=N= ( , , ) C. The unit binormal vector B=B= ( , , ) D. The curvature κ=κ=

Consider the spiral path x(t) = (cos^2t,sin^2t,t) for 0 ≤ t ≤ π/2. Evaluate the integral...

Consider the spiral path x(t) = (cos^2t,sin^2t,t) for 0 ≤ t ≤ π/2. Evaluate the integral x dx−y dy + z^2 dz

Given r(t) = <2 cos(t), 2 sin(t), 2t>. • What is the arc length of r(t)...

Given r(t) = <2 cos(t), 2 sin(t), 2t>. • What is the arc length of r(t) from t = 0 to t = 5. SET UP integral but DO NOT evaluate • What is the curvature κ(t)?

Consider the vector function given below. r(t) = 2t, 3 cos(t), 3 sin(t) (a) Find the...

Consider the vector function given below. r(t) = 2t, 3 cos(t), 3 sin(t) (a) Find the unit tangent and unit normal vectors T(t) and N(t). T(t) = N(t) = (b) Use this formula to find the curvature. κ(t) =

a) do the laplace transform to; x(t)= e^2t . sin(3t) . sin (t) b) do the...

a) do the laplace transform to; x(t)= e^2t . sin(3t) . sin (t) b) do the inverse laplace transform to; x(s) = (3s-5) / ( (s+1).(s^2+2s+5) )

Find the derivative of the function. A) f(x)=(2+x^3)^2/3 B) h(t)= (t^4-1)^9(t^3+1)^8 C) y = e4x sin(x)...

Find the derivative of the function. A) f(x)=(2+x^3)^2/3 B) h(t)= (t^4-1)^9(t^3+1)^8 C) y = e4x sin(x) D) y= (x^2+2/x^2-2)^3

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...

Question