f(t)=4e^(-3(t-4)) a) Find L[(df(t))/dt] by differentiating f(t) b) using the theorem for differentiation

ruigE 2020-11-08 Answered

Given that f(t)=4e3(t4)
a) Find L[df(t)dt] by differentiating f(t) and then using the Laplace transform tables in lecture notes.
b) Find L[df(t)dt] using the theorem for differentiation
c) Repeat a) and b) for the case that f(t)=4e3(t4)u(t4)

You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Brittany Patton
Answered 2020-11-09 Author has 100 answers
Step 1
According to the given information, the given function is:
f(t)=4e3(t4)
Step 2
For part (a) it is required to find Ldf(t)dt by differentiating f(t) and then using Laplace transform.
So,
df(t)dt=4e3(t4)(3)=12e3(t4)
L(dfdt)=L(12e3(t4))=L(12e3te12)
=12e12L(e3t)[L(eat)=1s+a]
L(dfdt)=12e12(1s+3)
Step 3
Now, it is required to find L(df(t)dt) using theorem for differentiation.
L(dfdt)=sL(f(t))f(0)
=s(L(4e3(t4)))4e3(04)
=s(L(4e3te12))4e12
=4se12L(e3t)4e12
=4se12(1s+3)4e12
=4e12(ss+31)
=4e12(s(s+3)s+3)
=4e12(3s+3)
L(dfdt)=12e12s+3
Step 4
Now, for part (c) it is required to repeat part (a) and (b) for the function:
f(t)=4e3(t4
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-02-25
A 1000 kg safe is 2.0 m above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it 50 cm. What is the spring constant of the spring?
asked 2020-11-01
As part of your work out, you lie on your back and push with your feet against a platform attached to two stiff springs arranged side by side so that they are parallel to each other. when u push the platform, you compress the springs. You do 80.0G of work when u compress the springs 0.200m from their uncompressed length.
a) What magnitude of force must u apply to hold the platform in this position?
b) How much additional work must you do to move the platform 0.200m farther, and what maximum force must you apply?
asked 2021-02-19

Two snowcats tow a housing unit to a new location at McMurdo Base, Antarctica, as shown in the figure. The sum of the forces FA and FB exerted on the unit by the horizontal cables is parallel to the line L, and FA=4200 N. Determine FB? Determine the magnitude of FA+FB?
asked 2021-02-20

An adventurous archaeologist crosses between two rock cliffs by slowly going hand-over-hand along a rope stretched between the cliffs. He stops to rest at the middle of the rope (Fig. 1) The rope will break if the tension in it exceeds 4.50104N and our hero's mass is 86.5 kg.

 Figure 1 a) If the angle θ is 13.0, find the tension iin the rope.

b) What is the smallest value the angle θ can have if the rope is not to break?

 
asked 2021-02-21
Object A is metallic and electrically neutral. It is chargedby induction so that it acquires a charge of 3.0106C.
Object B is identical to object A and is also electricallyneutral. It is carged by inductin so that it acquires a charge of +3.0106C.
Find the difference in massbetween the charged objects and state which has the greatermass.
asked 2021-05-10
A 2.0 kg mass is projected from the edge of the top of a 20mtall building with a velocity of 24m/s at some unknown angle abovethe horizontal. Disregard air resistance and assume the ground islevel. What is the kinetic energy of the mass just before itstrikes the ground?
asked 2021-08-12
The sixth assignment involves writing a Python program to read in from the user the temperatures for ten consecutive days in Celsius and store them into a Python data structure such as a list or a tuple. The entire list should then be displayed. Next each temperature in the list should be converted to Fahrenheit and stored in another data structure of the same type and the entire list should be again be displayed. The formula for converting Celsius to Fahrenheit is °F = (°C × 1.8) + 32. Finally, the number of cool, warm and hot days should be counted and the number of each type of days should be displayed. You should decide on the thresholds for determining whether a day is cool, warm or hot..

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question