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This is the impulse response:

Can anyone give a detailed method to prove that it is stable or not ?

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    $\begingroup$ Note that an impulse response cannot be stable or unstable. Stability is a property of a system, not its impulse response. $\endgroup$ – MBaz Nov 6 '14 at 23:20
  • $\begingroup$ Have you considered opening your textbook to see what, if anything, it says about the matter? Hint: it might be hidden in a definition such as “A system is said to be BIBO stable if it’s impulse response satisfies.......” $\endgroup$ – Dilip Sarwate Oct 27 at 17:23
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If you check graph of h(t) which is underdamped oscillations presrnt in 1st and 4th quadrant only. And integration of this h(t) from limits (-infinity to + infinity ) Is finite value. therefore, system is stable

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