control system

If δ(t)

δ(t) is a unit impulse function, which of the following is false?

• δ(0)≠0

• δ(10)=0

• δ(t)=0∀t

• none

If u(t)

u(t) is a unit step input, how is a delayed unit step input represented, taking a delay of a units?

• u(at)

• u(t−a)

• u(a−t)

• u(t+a)

Given x(t)=u(t)∗u(t),

what is x(10)

(∗ denotes convolution)

• 0

• 1

• 100

• 10

Consider a system with input x(t)

and output y(t)

related by

y(t)=x²(t)+x(t−3). The system is

• causal

• non causal

• time varying

• none

Consider a system with input

x(n) and output

y(n) related by

y(n)=cos⁡x(n) is the system linear?

• yes

• no

Which of the following is/are true about a dynamic system (Note: mutiple correct answer possible)

• memory elements are present

• no memory elements are present

• output depends on present input only

• output depends on present input and past input

In translational mechanical system, the damping is generally provided by

• static friction

• columb friction

• viscous friction

• spring friction

In order to double the time period of a simple pendulum, the length of the string should be

(Hint: The time period of a simple pendulum: It is defined as the time taken by the pendulum to finish one full oscillation)

• halved

• doubled

• quadrupled

• none

Using the initial value theorem of Laplace transform, the initial value of the function is

X(s)=s+1/s(s+2)

• 0

• 0.5

• 1

• 2

Using the final value theorem, the final value of given function is

X(s)=5s+4/s(5s+2)

• 1

• 2

• 2.5

• infinity