Impulse Response of LTI Systems

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ssquared

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I am trying to solve the attached question. Please I would appreciate if some one can check my approach and tell me if I am correct and how can I proceed in getting h0(t)
 

At the final expression of H(s), the exponential has -s*T1 which represents a delay.
Impulse response=1 from 0 to T1 and then 0 from T1 to infinity.
Step response = linear ramp from 0 to T1 and then is T1 from T1 to infinity.

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Please I would appreciate if some one can check my approach and tell me if I am correct ...
Your approach is correct.
 

I have used the expression of h(t) to derive H(jw) and I got the exact expression
 

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