Question

In: Advanced Math

Please help me to conceive and designing an engineering mathmatical which can use laplace transform, the...

Please help me to conceive and designing an engineering mathmatical which can use laplace transform, the problem closed to our daily live is best.

Solutions

Expert Solution

1) One uses the Laplace transform to study the transient response of a circuit. Like, when you turn it on, what happens as current flows to charge the capacitors in the circuit to their normal operating voltage. With the proper use of the transform one can see the transient voltage drop in each resistor caused by the charging current.

For the steady state response one uses the Fourier transform, which has many similarities with the Laplace transform.

2) I can't really give you a good example a problem where you need it exactly, but I can maybe try to explain why it's useful. The LaPlace transform takes a differential equation and turns it into a linear equation, so it's easier to solve by algebra, rather than calculus. Then we can take the inverse LaPlace transform and solve for the answer.

3) Laplace transform is integral transform named after its discoverer named Pierre Simon Laplace. It can be used as follows:

It is used in nuclear physics.

It is used in determining structure of astronomical object from spectrum

4) Stability is a concern in any 'real' system. So yes, Laplace transform is used in real life.

If your question is 'Why is the Laplace transform used for stability analysis?', then take a look at my answers here:


Related Solutions

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!
Use Laplace Transform to solve the initial value problem. Please show all work and steps clearly...
Use Laplace Transform to solve the initial value problem. Please show all work and steps clearly so I can follow your logic and learn to solve similar ones myself. I will also rate your answer. Thank you kindly! y′′ + 4y = f(t), y(0) = 0, y′(0) = 0, where;  f(t)= 1 if 1 ≤ t < 2, 0 otherwise
can anyone please help me woth graphs and business report for business computing?
can anyone please help me woth graphs and business report for business computing?
Corporate governance is a tough process for me to grasp. Please help me understand this by...
Corporate governance is a tough process for me to grasp. Please help me understand this by discussing the relevance of corporate governance. What does it look like? How can a company benefit from governance systems; i.e. what benefits are provided to decision makers? If possible please provide an industry example of corporate governance that you know of or have been involved in from research to further help explain this concept. Thanks!
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.
Use the Laplace transform to solve the following initial value problem, y′′ − y′ − 30y  ...
Use the Laplace transform to solve the following initial value problem, y′′ − y′ − 30y  =  δ(t − 7),y(0)  =  0,  y′(0)  =  0. The solution is of the form ?[g(t)] h(t). (a) Enter the function g(t) into the answer box below. (b) Enter the function h(t) into the answer box below.
Use the Laplace transform to solve the given initial-value problem. y'' − 7y' = 12e6t −...
Use the Laplace transform to solve the given initial-value problem. y'' − 7y' = 12e6t − 6e−t,    y(0) = 1, y'(0) = −1
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...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT