Physics Exam > Physics Questions > A particle is executing SHM. If the displacem...
Start Learning for Free
A particle is executing SHM. If the displacement at any instant is given by x = 3 c o s 2 + 4 s in 2 t. What is the time period of the particle?
- a)1.57 S
- b)2 S
- c)3.14 S
- d)5 S
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A particle is executing SHM. If the displacement at any instant is giv...
x = 3 cos 2t + 4 sin 2t
x = 3 cos 2t + 4 sin 2t
⇒ ω = 2
x = 3 cos 2t + 4 sin 2t
⇒ ω = 2
Most Upvoted Answer
A particle is executing SHM. If the displacement at any instant is giv...
x = 3 cos 2t + 4 sin 2t
x = 3 cos 2t + 4 sin 2t
⇒ ω = 2
x = 3 cos 2t + 4 sin 2t
⇒ ω = 2
Free Test
FREE
| Start Free Test |
Community Answer
A particle is executing SHM. If the displacement at any instant is giv...
Given:
The displacement of a particle executing Simple Harmonic Motion (SHM) is given by the equation: x = 3cos(2πt) + 4sin(2πt)
To Find:
The time period of the particle.
Explanation:
1. Equation of SHM:
The general equation for SHM is given by:
x = A cos(ωt + φ)
where,
x = displacement of the particle
A = amplitude of the motion
ω = angular frequency of the motion
t = time
φ = phase constant
In the given equation, x = 3cos(2πt) + 4sin(2πt), we can rewrite it by combining the sine and cosine terms:
x = A cos(ωt + φ)
Comparing the terms, we can see that:
A = √(3^2 + 4^2) = 5
ωt + φ = 2πt
2. Relationship between Time Period and Angular Frequency:
The time period (T) is the time taken to complete one full oscillation. The angular frequency (ω) is related to the time period by the equation:
T = 2π/ω
3. Finding the Time Period:
From the equation, ωt + φ = 2πt, we can equate the coefficients of t:
ωt = 2πt
This implies that ω = 2π, which is the angular frequency of the particle.
Using the relationship between time period and angular frequency, we can find the time period:
T = 2π/ω
T = 2π/(2π)
T = 1
4. Answer:
The time period of the particle is 1 second, which corresponds to option (b) in the given choices.
The displacement of a particle executing Simple Harmonic Motion (SHM) is given by the equation: x = 3cos(2πt) + 4sin(2πt)
To Find:
The time period of the particle.
Explanation:
1. Equation of SHM:
The general equation for SHM is given by:
x = A cos(ωt + φ)
where,
x = displacement of the particle
A = amplitude of the motion
ω = angular frequency of the motion
t = time
φ = phase constant
In the given equation, x = 3cos(2πt) + 4sin(2πt), we can rewrite it by combining the sine and cosine terms:
x = A cos(ωt + φ)
Comparing the terms, we can see that:
A = √(3^2 + 4^2) = 5
ωt + φ = 2πt
2. Relationship between Time Period and Angular Frequency:
The time period (T) is the time taken to complete one full oscillation. The angular frequency (ω) is related to the time period by the equation:
T = 2π/ω
3. Finding the Time Period:
From the equation, ωt + φ = 2πt, we can equate the coefficients of t:
ωt = 2πt
This implies that ω = 2π, which is the angular frequency of the particle.
Using the relationship between time period and angular frequency, we can find the time period:
T = 2π/ω
T = 2π/(2π)
T = 1
4. Answer:
The time period of the particle is 1 second, which corresponds to option (b) in the given choices.
|
Explore Courses for Physics exam
|
|
Similar Physics Doubts
A particle is executing SHM. If the displacement at any instant is given by x = 3 c o s 2 + 4 s in 2 t. What is the time period of the particle?a)1.57 Sb)2 Sc)3.14 Sd)5 SCorrect answer is option 'C'. Can you explain this answer?
Question Description
A particle is executing SHM. If the displacement at any instant is given by x = 3 c o s 2 + 4 s in 2 t. What is the time period of the particle?a)1.57 Sb)2 Sc)3.14 Sd)5 SCorrect answer is option 'C'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A particle is executing SHM. If the displacement at any instant is given by x = 3 c o s 2 + 4 s in 2 t. What is the time period of the particle?a)1.57 Sb)2 Sc)3.14 Sd)5 SCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is executing SHM. If the displacement at any instant is given by x = 3 c o s 2 + 4 s in 2 t. What is the time period of the particle?a)1.57 Sb)2 Sc)3.14 Sd)5 SCorrect answer is option 'C'. Can you explain this answer?.
A particle is executing SHM. If the displacement at any instant is given by x = 3 c o s 2 + 4 s in 2 t. What is the time period of the particle?a)1.57 Sb)2 Sc)3.14 Sd)5 SCorrect answer is option 'C'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A particle is executing SHM. If the displacement at any instant is given by x = 3 c o s 2 + 4 s in 2 t. What is the time period of the particle?a)1.57 Sb)2 Sc)3.14 Sd)5 SCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is executing SHM. If the displacement at any instant is given by x = 3 c o s 2 + 4 s in 2 t. What is the time period of the particle?a)1.57 Sb)2 Sc)3.14 Sd)5 SCorrect answer is option 'C'. Can you explain this answer?.
Solutions for A particle is executing SHM. If the displacement at any instant is given by x = 3 c o s 2 + 4 s in 2 t. What is the time period of the particle?a)1.57 Sb)2 Sc)3.14 Sd)5 SCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Physics.
Download more important topics, notes, lectures and mock test series for Physics Exam by signing up for free.
Here you can find the meaning of A particle is executing SHM. If the displacement at any instant is given by x = 3 c o s 2 + 4 s in 2 t. What is the time period of the particle?a)1.57 Sb)2 Sc)3.14 Sd)5 SCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A particle is executing SHM. If the displacement at any instant is given by x = 3 c o s 2 + 4 s in 2 t. What is the time period of the particle?a)1.57 Sb)2 Sc)3.14 Sd)5 SCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A particle is executing SHM. If the displacement at any instant is given by x = 3 c o s 2 + 4 s in 2 t. What is the time period of the particle?a)1.57 Sb)2 Sc)3.14 Sd)5 SCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A particle is executing SHM. If the displacement at any instant is given by x = 3 c o s 2 + 4 s in 2 t. What is the time period of the particle?a)1.57 Sb)2 Sc)3.14 Sd)5 SCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A particle is executing SHM. If the displacement at any instant is given by x = 3 c o s 2 + 4 s in 2 t. What is the time period of the particle?a)1.57 Sb)2 Sc)3.14 Sd)5 SCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Physics tests.
|
|
Explore Courses for Physics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup