GATE 2015 EE – SET 2 – Question 4

Solution :

$$f(t) $$ = 2$$\sqrt{\frac{t}{T}}$$

$${f}'(t)$$=$$ \frac{2}{\sqrt{\pi }} . \frac{1}{2\sqrt{t}}$$

$$\Rightarrow $$$$\frac{1}{\sqrt{\pi }t}$$

$$\Rightarrow $$$$\sqrt{\frac{1}{\pi t}}$$

$$\Rightarrow$$ $$g(t) $$

$$L\left [ {f}'(t) \right ] $$= SL $$\left [ f(t) \right ]$$ – f (0)

$$L\left [ {f}'(t) \right ] $$ = ┬áS$$\left [ S^{\frac{-3}{2}} \right ] – 2\sqrt{\frac{0}{\pi }}$$

$$S^{1}(S^{\frac{-3}{2}})$$ = $$S ^{\frac{-1}{2}}$$