Multiple Choice Questions:
- Which of the following excitation functions yields a response that can be directly obtained from convolution with the system’s impulse response?
a) Unit impulse
b) Arbitrary force
c) Step force
d) Rectangular pulse force
Answer: a) Unit impulse
Explanation: The response to a unit impulse excitation can be directly obtained by convolving the impulse response of the system with the unit impulse function. - Which method is commonly used to analyze the response of linear time-invariant systems to arbitrary excitation functions?
a) Fourier transform
b) Laplace transform
c) Duhamel’s integral
d) Convolution theorem
Answer: c) Duhamel’s integral
Explanation: Duhamel’s integral is commonly used to find the response of linear time-invariant systems to arbitrary excitation functions. - For which type of excitation is the step response particularly useful in analyzing system behavior?
a) Mechanical systems
b) Electrical circuits
c) Hydraulic systems
d) Thermal systems
Answer: b) Electrical circuits
Explanation: The step response is particularly useful in analyzing the behavior of electrical circuits. - Which excitation function results in a response that can be calculated using the principle of superposition?
a) Unit impulse
b) Step force
c) Rectangular pulse force
d) Triangular pulse force
Answer: d) Triangular pulse force
Explanation: The response to a triangular pulse force can be calculated using the principle of superposition because it can be seen as the sum of multiple step functions. - Which method is used to calculate the response of linear time-invariant systems to arbitrary force inputs, considering both initial conditions and the force history?
a) Fourier series
b) Laplace transform
c) Duhamel’s integral
d) Convolution theorem
Answer: c) Duhamel’s integral
Explanation: Duhamel’s integral takes into account both the initial conditions and the force history to calculate the response of linear time-invariant systems to arbitrary force inputs. - Which excitation function has a response characterized by a sudden change followed by a constant value?
a) Unit impulse
b) Step force
c) Rectangular pulse force
d) Half cycle sinusoidal pulse force
Answer: b) Step force
Explanation: The step force excitation function results in a response characterized by a sudden change followed by a constant value. - For which type of system is the response to a rectangular pulse force often analyzed?
a) Mechanical systems
b) Control systems
c) Fluid dynamics systems
d) Communication systems
Answer: d) Communication systems
Explanation: The response to a rectangular pulse force is often analyzed in communication systems, especially in signal processing. - Which excitation function results in a response that can be decomposed into a series of sinusoidal components through Fourier analysis?
a) Unit impulse
b) Arbitrary force
c) Half cycle sinusoidal pulse force
d) Triangular pulse force
Answer: c) Half cycle sinusoidal pulse force
Explanation: The response to a half cycle sinusoidal pulse force can be decomposed into sinusoidal components using Fourier analysis. - Which type of excitation function results in a response characterized by a continuous change in magnitude and direction?
a) Step force
b) Rectangular pulse force
c) Half cycle sinusoidal pulse force
d) Triangular pulse force
Answer: d) Triangular pulse force
Explanation: The response to a triangular pulse force is characterized by a continuous change in magnitude and direction. - Which method is particularly useful for calculating the response of linear time-invariant systems to periodic excitation functions?
a) Laplace transform
b) Fourier series
c) Convolution theorem
d) Duhamel’s integral
Answer: b) Fourier series
Explanation: Fourier series is particularly useful for analyzing the response of linear time-invariant systems to periodic excitation functions, as it decomposes periodic functions into a sum of sinusoidal functions.