Mechanical Engineering Exam  >  Mechanical Engineering Questions  >  X(t) is a real valued function of a real vari... Start Learning for Free
X(t) is a real valued function of a real variable with period T. Its trigonometric Fourier Series expansion contains no terms of frequency ω = 2π (2k ) /T ; k = 1, 2,.... Also, no sine terms are present. Then x(t) satisfies the equation 
  • a)
    x ( t ) =−x(t − T)
  • b)
    x (t) = −x(T − t)= −x (−t)
  • c)
    x (t) = x(T− t) = −x (t −T / 2)
  • d)
    x (t ) = x(t−T) = x (t −T / 2)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
X(t) is a real valued function of a real variable with period T. Its t...
No sine terms are present.
∴x(t ) is even function.
View all questions of this test
Most Upvoted Answer
X(t) is a real valued function of a real variable with period T. Its t...
Option C seems to be correct. As they gave that the given signal doesn't contain the even harmonics, which means that the signal has odd half wave Symmetry.
Hence x(t) = -x(t-T/2).
And as the signal is even signal. x(t) = x(t-T) = x(T-t)= -x(t-T/2).
Free Test
Community Answer
X(t) is a real valued function of a real variable with period T. Its t...
Given Information:
- X(t) is a real-valued function of a real variable with period T.
- The trigonometric Fourier Series expansion of X(t) contains no terms of frequency ω = 2(2k)π/T, where k = 1, 2, ...
- No sine terms are present in the Fourier Series expansion of X(t).

To Find:
The equation satisfied by x(t).

Solution:
Let's analyze the given conditions and determine the equation satisfied by x(t).

1. No terms of frequency ω = 2(2k)π/T:
The Fourier Series expansion of a periodic function X(t) is given by:
X(t) = a0/2 + Σ[ak*cos(kω0t) + bk*sin(kω0t)]
where ω0 = 2π/T is the fundamental frequency.

Since there are no terms of frequency ω = 2(2k)π/T in the Fourier Series of X(t), it implies that ak = 0 for all k.

2. No sine terms are present:
Since no sine terms are present in the Fourier Series of X(t), it implies that bk = 0 for all k.

3. Implication of ak = 0 and bk = 0:
When ak = 0 and bk = 0 for all k, the Fourier Series expansion of X(t) simplifies to:
X(t) = a0/2

4. Simplification of the Fourier Series expansion:
From the previous step, we have X(t) = a0/2.

Comparing this with the general form of the Fourier Series expansion, we can deduce that the constant term a0/2 represents the average value of X(t) over one period.

5. Equation satisfied by x(t):
Since X(t) represents the average value of X(t) over one period, it implies that X(t) is a constant function. Let's denote this constant value as C.

Therefore, the equation satisfied by x(t) is:
x(t) = C

Conclusion:
The equation satisfied by x(t) is x(t) = C, where C is a constant. Therefore, the correct answer is option 'D' - x(t) = x(tT) = x(tT/2).
Attention Mechanical Engineering Students!
To make sure you are not studying endlessly, EduRev has designed Mechanical Engineering study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Mechanical Engineering.
Explore Courses for Mechanical Engineering exam

Top Courses for Mechanical Engineering

X(t) is a real valued function of a real variable with period T. Its trigonometric Fourier Series expansion contains no terms of frequency ω = 2π (2k ) /T ; k = 1, 2,.... Also, no sine terms are present. Then x(t) satisfies the equationa)x ( t ) =−x(t − T)b)x (t) = −x(T − t)= −x (−t)c)x (t) = x(T− t) = −x (t −T / 2)d)x (t ) = x(t−T) = x (t −T / 2)Correct answer is option 'D'. Can you explain this answer?
Question Description
X(t) is a real valued function of a real variable with period T. Its trigonometric Fourier Series expansion contains no terms of frequency ω = 2π (2k ) /T ; k = 1, 2,.... Also, no sine terms are present. Then x(t) satisfies the equationa)x ( t ) =−x(t − T)b)x (t) = −x(T − t)= −x (−t)c)x (t) = x(T− t) = −x (t −T / 2)d)x (t ) = x(t−T) = x (t −T / 2)Correct answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about X(t) is a real valued function of a real variable with period T. Its trigonometric Fourier Series expansion contains no terms of frequency ω = 2π (2k ) /T ; k = 1, 2,.... Also, no sine terms are present. Then x(t) satisfies the equationa)x ( t ) =−x(t − T)b)x (t) = −x(T − t)= −x (−t)c)x (t) = x(T− t) = −x (t −T / 2)d)x (t ) = x(t−T) = x (t −T / 2)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for X(t) is a real valued function of a real variable with period T. Its trigonometric Fourier Series expansion contains no terms of frequency ω = 2π (2k ) /T ; k = 1, 2,.... Also, no sine terms are present. Then x(t) satisfies the equationa)x ( t ) =−x(t − T)b)x (t) = −x(T − t)= −x (−t)c)x (t) = x(T− t) = −x (t −T / 2)d)x (t ) = x(t−T) = x (t −T / 2)Correct answer is option 'D'. Can you explain this answer?.
Solutions for X(t) is a real valued function of a real variable with period T. Its trigonometric Fourier Series expansion contains no terms of frequency ω = 2π (2k ) /T ; k = 1, 2,.... Also, no sine terms are present. Then x(t) satisfies the equationa)x ( t ) =−x(t − T)b)x (t) = −x(T − t)= −x (−t)c)x (t) = x(T− t) = −x (t −T / 2)d)x (t ) = x(t−T) = x (t −T / 2)Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering. Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of X(t) is a real valued function of a real variable with period T. Its trigonometric Fourier Series expansion contains no terms of frequency ω = 2π (2k ) /T ; k = 1, 2,.... Also, no sine terms are present. Then x(t) satisfies the equationa)x ( t ) =−x(t − T)b)x (t) = −x(T − t)= −x (−t)c)x (t) = x(T− t) = −x (t −T / 2)d)x (t ) = x(t−T) = x (t −T / 2)Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of X(t) is a real valued function of a real variable with period T. Its trigonometric Fourier Series expansion contains no terms of frequency ω = 2π (2k ) /T ; k = 1, 2,.... Also, no sine terms are present. Then x(t) satisfies the equationa)x ( t ) =−x(t − T)b)x (t) = −x(T − t)= −x (−t)c)x (t) = x(T− t) = −x (t −T / 2)d)x (t ) = x(t−T) = x (t −T / 2)Correct answer is option 'D'. Can you explain this answer?, a detailed solution for X(t) is a real valued function of a real variable with period T. Its trigonometric Fourier Series expansion contains no terms of frequency ω = 2π (2k ) /T ; k = 1, 2,.... Also, no sine terms are present. Then x(t) satisfies the equationa)x ( t ) =−x(t − T)b)x (t) = −x(T − t)= −x (−t)c)x (t) = x(T− t) = −x (t −T / 2)d)x (t ) = x(t−T) = x (t −T / 2)Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of X(t) is a real valued function of a real variable with period T. Its trigonometric Fourier Series expansion contains no terms of frequency ω = 2π (2k ) /T ; k = 1, 2,.... Also, no sine terms are present. Then x(t) satisfies the equationa)x ( t ) =−x(t − T)b)x (t) = −x(T − t)= −x (−t)c)x (t) = x(T− t) = −x (t −T / 2)d)x (t ) = x(t−T) = x (t −T / 2)Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice X(t) is a real valued function of a real variable with period T. Its trigonometric Fourier Series expansion contains no terms of frequency ω = 2π (2k ) /T ; k = 1, 2,.... Also, no sine terms are present. Then x(t) satisfies the equationa)x ( t ) =−x(t − T)b)x (t) = −x(T − t)= −x (−t)c)x (t) = x(T− t) = −x (t −T / 2)d)x (t ) = x(t−T) = x (t −T / 2)Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
Explore Courses for Mechanical Engineering exam

Top Courses for Mechanical Engineering

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev