Question

4. (a) Using convolution, find the inverse Laplace transform of \frac{10}{s(s+2)}, $-S(e^{-2t}-1)$ (b) A metal bar at a temperature of 100° F is placed in a room at a constant temperature of 0° F. If after 20 minutes the temperature of the bar is 50° F, find the temperature of the bar after 10 minutes. $\theta = 70 - 8$

          4. (a) Using convolution, find the inverse Laplace transform of \frac{10}{s(s+2)}, $-S(e^{-2t}-1)$ 
(b) A metal bar at a temperature of 100° F is placed in a room at a constant temperature of 0° F. If after 20 minutes the temperature of the bar is 50° F, find the temperature of the bar after 10 minutes. $\theta = 70 - 8$

4. (a) Using convolution, find the inverse Laplace transform of (10)/(s(s+2)), -S(e^-2t-1)
(b) A metal bar at a temperature of 100° F is placed in a room at a constant temperature of 0° F. If after 20 minutes the temperature of the bar is 50° F, find the temperature of the bar after 10 minutes. θ = 70 - 8

Added by Daniel N.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

12/22/2023

Step 1

Given function: F(s) = 10/(s(s+2)) We know that the Laplace transform of the unit step function u(t) is 1/s. Therefore, the Laplace transform of u(t-2) is e^(-2s)/s. Using the convolution property of Laplace transforms, we can write the inverse Laplace Show more…

Show all steps

Thanks for your feedback!

A. (a) Using convolution, find the inverse Laplace transform of [5] (10)/(s(s+2)) (b) A metal bar at a temperature of 100deg F is placed in a room at a constant temperature of 0deg F. If after 20 minutes the temperature of the bar is 50deg F, find the temperature of the bar after 10 minutes. aUsing convolution,find the inverse Laplace transform of [5] 10 -s(e-2t s(s+2 (b A metal bar at a temperature of 100 F is placed in a room at a constant temperature of 0F.If after 20 minutes the temperature of the bar is50 F,find the temperature of the bar after 10 minutes. [5] =10-8