codproplayd
New member
- Joined
- Oct 31, 2019
- Messages
- 2
Hello,
I know that to integrate Newton's law of cooling's differential equation T′(t)=k(T(t)−A) where T=temperature, t=time, A=constant temperature of the surrounding, and k is constant, I can use Laplace transform:
T′(t)=K⋅(T(t)−A)→s⋅T(s)−T(0)=K⋅(T(s)−A⋅1/s)
Then solve for T (s) and use the inverse transform.
T(s)=(T(0)−K⋅A⋅(1/s))/(s−K) => T(t)=A+e^Kt(T(0)−A) correct me if I am mistaken please
And from there I could solve the equation, which is easy, but I don't know the step-by-step method of using both the Laplace transform and inverse with adding the integrals to clearly explain what I did on paper.
I would be thankful if someone would help me out with this one
I know that to integrate Newton's law of cooling's differential equation T′(t)=k(T(t)−A) where T=temperature, t=time, A=constant temperature of the surrounding, and k is constant, I can use Laplace transform:
T′(t)=K⋅(T(t)−A)→s⋅T(s)−T(0)=K⋅(T(s)−A⋅1/s)
Then solve for T (s) and use the inverse transform.
T(s)=(T(0)−K⋅A⋅(1/s))/(s−K) => T(t)=A+e^Kt(T(0)−A) correct me if I am mistaken please
And from there I could solve the equation, which is easy, but I don't know the step-by-step method of using both the Laplace transform and inverse with adding the integrals to clearly explain what I did on paper.
I would be thankful if someone would help me out with this one