Question
In: Advanced Math
Use laplace transform in solving the ff.: After cooking for 45 minutes, when a cake is...
Use laplace transform in solving the ff.:
After cooking for 45 minutes, when a cake is removed from an oven its temperature is measured at 300°F. 3 minutes later its temperature is 200°F. The oven is not preheated, so at t=0, when the cake mixture is placed into the oven, the temperature inside the oven is also 70°F. The temperature of the oven increases linearly until t=4 minutes, when the desired temperature of 300°F is attained; thereafter the oven temperature is constant 300°F for t is greater than pr equal to 4 minutes.
a.) devised a mathematical model for the temperature of a cake while it is inside the oven and after it is taken out of the oven.
b.) how long will it take the cake to cool off to a room temperature of 70°F
Solutions
Colby Messinger answered 2 years agoRelated Solutions
Use laplace Transform in solving the ff.: After cooking for 45 minutes, when a cake is...
Use laplace Transform in solving the ff.:
After cooking for 45 minutes, when a cake is removed
from an oven its temperature is measured at 300°F. 3 minutes later
its temperature is 200°F. The oven is pre heated, and so at t=0,
the cake mixture is at the room temperature of 70°F. The
temperature of the oven increases linearly until t=4 minutes, when
the desired temperature of 300°F is attained; thereafter the oven
temperature is constant 300°F for t is...
Use Laplace Tranform in solving the ff.: After cooking for 45 minutes, when a cake is...
Use Laplace Tranform in solving the ff.:
After cooking for 45 minutes, when a cake is removed
from an oven, its temperature is measured at 300°F. 3 minutes
later, its temperature is 200°F. The oven is preheated, and so at
t=0, the cake mixture is at the room temperature of 70°F. The
temperature of the oven increases linearly until t=4 minutes, when
the desired temperature of 300°F is attained; thereafter the oven
temperature is constant 300°F for t is greater...
Solving Differential Equations using Laplace Transform
Solving Differential Equations using Laplace Transform
a) y" - y' -2y = 0
y(0) = 1, y'(0) = 0
answer: y = 1/3e^2t + 2/3e^-t
b) y" + y = sin2t
y(0) = 2, y'(0) = 1
answer: y(t) = 2cost + 5/3 sint - 1/3sin2t
c) y^4 - y = 0
y(0) = 0, y'(0) = 1, y"(0) = 0, y'''(0) = 0
answer y(t) = (sinht + sint)/2
3) Laplace Transform and Solving first order Linear Differential Equations with Applications The Laplace transform of...
3) Laplace Transform and Solving first order Linear Differential
Equations with Applications The Laplace transform of a function,
transform of a derivative, transform of the second derivative,
transform of an integral, table of Laplace transform for simple
functions, the inverse Laplace transform, solving first order
linear differential equations by the Laplace transform
Applications: a)))))) Series RL circuit with
ac source [electronics]
4) Laplace Transform and Solving second order Linear Differential Equations with Applications The Laplace transform of...
4) Laplace Transform and Solving second order Linear
Differential Equations with Applications The Laplace transform of a
function, transform of a derivative, transform of the second
derivative, transform of an integral, table of Laplace transform
for simple functions, the inverse Laplace transform, solving first
order linear differential equations by the Laplace transform
Applications: a) Series RLC circuit with dc source b) Damped
motion of an object in a fluid [mechanical, electromechanical] c)
Forced Oscillations [mechanical, electromechanical]
You should build the...
write the theory and formulas for solving the systems of equations using the Laplace transform. Must...
write the theory and formulas for solving the systems of
equations using the Laplace transform. Must contain
bibliography
Use Laplace transform and inverse Laplace transform to solve the givien initial value problems (c) y′′...
Use
Laplace transform and inverse Laplace transform to solve the givien
initial value problems
(c) y′′ −2y′ +2y=e−t, y(0)=0, y′(0)=1
Use the table of Laplace Transform along with the two properties to compute the following laplace...
Use the table of Laplace Transform along with the two properties
to compute the following laplace transforms. (Hint: Trig identities
may be useful for some).
(a) sin(2t)+ cos(4t)
(b) sin(t + π/4)
(c) cosh(t)*sin(t) (recall cosh(t) := e t+e −t 2 )
Use the Laplace transform to find the solution of the IVP: a.) 2y' + y =...
Use the Laplace transform to find the solution of the IVP:
a.) 2y' + y = 1, y(0) = 2 (answer should be y(t) = 1 + e-t
/ 2 )
f.) 4y" + y = 0, y(0) = -1, y'(0) = -1 (answer should be y(t) =
-sin(t) - cos(t))
Please show work!
Q1. What is Laplace transform and why do we use it in circuit analysis.
Q1.
What is Laplace transform and why do we use it in circuit
analysis.
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