Exams › GATE › Technical

An LTI system is shown in the figure where G(s) = 100/(s² + 0.1s + 10). The steady state output of the system, to the input r(t), is given as y(t) = a + b sin(10t + θ). The values of ‘a’ and ‘b’ will be

1. a = 1, b = 10
2. a = 10, b = 1
3. a = 1, b = 100
4. a = 100, b = 1

Correct answer: a = 1, b = 10

Solution

The steady state output of an LTI system to a sinusoidal input can be determined using the system's frequency response. For the given transfer function, at the frequency of the input (10 rad/s), the output has a DC component of 1 and an amplitude of 10 for the sinusoidal part, leading to the values a = 1 and b = 10.

Related GATE Technical questions

• For an ideal MOSFET biased in saturation, the magnitude of the small signal current gain for a common drain amplifier is
• The most commonly used relay, for the protection of an alternator against loss of excitation, is
• The geometric mean radius of a conductor, having four equal strands with each strand of radius ‘r’, as shown in the figure below, is
• The Bode magnitude plot of a first order stable system is constant with frequency. The asymptotic value of the high frequency phase, for the system, is −180°. This system has
• In the circuit shown below, a three-phase star-connected unbalanced load is connected to a balanced three-phase supply of 100√3 V with phase sequence ABC. The star connected load has Z_A = 10 Ω and Z_B = 20∠60° Ω. The value of Z_C in Ω, for which the voltage difference across the nodes n and n' is zero, is
• A charger supplies 100 W at 20 V for charging the battery of a laptop. The power devices, used in the converter inside the charger, operate at a switching frequency of 200 kHz. Which power device is best suited for this purpose?

⚔️ Practice GATE Technical free + battle 1v1 →