Physical Meaning of T's in Laplace equations

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The discussion focuses on understanding the physical meaning of the time constant T in Laplace equations, specifically in the context of integrators and transfer functions. The equation 1/sT represents an integrator with a time constant, where a unit step input results in an output reaching unity in T seconds. Participants seek clarification on the meaning of T in the equations Signal = 1/(1+sT) and Signal = 1/(1+s*T1+s^2*T2), noting that T typically represents sampling time. Additionally, there is a request for assistance in finding the Laplace inverse of these signals. The conversation emphasizes the importance of T in determining system behavior in control theory.
RadKrish
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Dear All,

When I have a equation 1/sT
its an integrator with time constant
i.e Assuming a T of 5s, if I input a unit step function, the output of the integrator reaches unity in 5 seconds

atleast I undestand it that way. Please correct me if I am wrong
in the same way can someone help me to understnd the physical meaning of T in the following equation

Signal = 1/(1+sT) and Signal = 1/(1+ s*T1 +s^2*T2)
also kindly help me to find the lapalace inverse of the above signals!
 
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usually that T means the sampling time. s is not a dimensionless quantity but sT is dimensionless.
 

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