The signal xt is defined asxt-5sint- 0-t- t-2 -t-2- t-2 2-t-3- 0- otherwiseThe energy in the signal is -

E=∫^∞_ ∞|x(t)|^2dt E=25∫^π_0sin^2t dt+∫^2π_π(t+2)^2dt+∫^3π_2π(t 2)^2dt E=25∫^π_0(1 cos2t2)dt+[(t+2)^33]^2π_π+[(t 2)^33]^3π_2π E=25(π2)+(2π+2)^3 (π+2)^33+(3π ...

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Standard X

Physics

Circuit diagram & commonly used symbols

The signal xt...

Question

The signal x(t) is defined as

x(t)= $⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} 5 s i n t, & 0 < t < π t + 2 & π < t < 2 π t - 2 & 2 π < t < 3 π 0, & o t h e r w i s e \end{matrix}$

The energy in the signal is _______.
293.64

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Solution

The correct option is A 293.64
$E = \int_{- \infty}^{\infty} | x (t) |^{2} d t$

$E = 25 \int_{0}^{π} s i n^{2} t d t + \int_{π}^{2 π} (t + 2)^{2} d t + \int_{2 π}^{3 π} (t - 2)^{2} d t$

$E = 25 \int_{0}^{π} (\frac{1 - c o s 2 t}{2}) d t + {[\frac{(t + 2)^{3}}{3}]}_{π}^{2 π} + {[\frac{(t - 2)^{3}}{3}]}_{2 π}^{3 π}$

$E = 25 (\frac{π}{2}) + \frac{(2 π + 2)^{3} - (π + 2)^{3}}{3} + \frac{(3 π - 2)^{3} - (2 π - 2)^{3}}{3} = 293.64$

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The signal x(t) is defined as x(t)=⎧⎪ ⎪⎨⎪ ⎪⎩5sint,0<t<πt+2π<t<2πt−22π<t<3π0,otherwise The energy in the signal is _______.293.64

The correct option is A 293.64E=∫∞−∞|x(t)|2dt E=25∫π0sin2tdt+∫2ππ(t+2)2dt+∫3π2π(t−2)2dt E=25∫π0(1−cos2t2)dt+[(t+2)33]2ππ+[(t−2)33]3π2π E=25(π2)+(2π+2)3−(π+2)33+(3π−2)3−(2π−2)33=293.64

The signal x(t) is defined as

x(t)= $⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} 5 s i n t, & 0 < t < π t + 2 & π < t < 2 π t - 2 & 2 π < t < 3 π 0, & o t h e r w i s e \end{matrix}$

The energy in the signal is _______.
293.64