Physical Meaning of T's in Laplace equations

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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.