GATE EE 2012 Question Paper (12-Feb-2012) (Shift 2)

State variable description of an LTI system is given by

≤ft[ {*20c {x_1}\\ {x_2}\\ {x_3} } ] = ≤ft[ {*20c 0&a_1&0\\ 0&0&a_2\\ a_3&0&0 } ]≤ft[ {*20c x_1\\ x_3\\ x_3 } ] + ≤ft[ {*20c 0\\ 0\\ 1 } ]U

Y = ≤ft[ {*20c 1&0&0 } ]≤ft[ {*20c x_1\\ x_2\\ x_3 } ]

Where Y is the output and u is input. System is controllable for

The Fourier transform of a signal h(t) is H (jω) = (2 cosω ) (sin2ω) / ω . The value of h(0) is

The feedback system shown below oscillates at 2 rads/sec. when

The input x(t) and output y(t) of a system are related as $y(t)={\int }_{-\infty }^{t}x(\tau )cos(3\tau )d\tau .$ The system is

An analog voltmeter uses external multiplier setting with a multiplier setting of 20 kΩ, it reads 440 V and with a multiplier setting of 80 kΩ it reads 352 V. For a multiplier setting of 40 kΩ the voltmeter reads______.