Menu Close

find-all-function-that-satisfy-p-gt-0-0-f-t-e-pt-dt-e-pT-with-T-a-positive-real-




Question Number 77536 by ~blr237~ last updated on 07/Jan/20
find all function that satisfy    ∀ p>0   ∫_0 ^∞ f(t)e^(−pt) dt= e^(−pT)       with T a positive real
$$\mathrm{find}\:\mathrm{all}\:\mathrm{function}\:\mathrm{that}\:\mathrm{satisfy} \\ $$$$\:\:\forall\:\mathrm{p}>\mathrm{0}\:\:\:\int_{\mathrm{0}} ^{\infty} \mathrm{f}\left(\mathrm{t}\right)\mathrm{e}^{−\mathrm{pt}} \mathrm{dt}=\:\mathrm{e}^{−\mathrm{pT}} \:\:\:\:\:\:\mathrm{with}\:\mathrm{T}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{real} \\ $$
Answered by JDamian last updated on 07/Jan/20
According to the Laplace Transform  tables    f(t)=δ(t−T)    which is known as delayed impulse.
$${According}\:{to}\:{the}\:\boldsymbol{{Laplace}}\:\boldsymbol{{Transform}} \\ $$$${tables} \\ $$$$ \\ $$$${f}\left({t}\right)=\delta\left({t}−{T}\right) \\ $$$$ \\ $$$${which}\:{is}\:{known}\:{as}\:\boldsymbol{{delayed}}\:\boldsymbol{{impulse}}. \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *