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In a certain oscillatory system,the amplitude pf motion is 5m and the time period is 4s.The time taken by the particle for passing between poits which are at distances of 4m and 2m from the center and on the same side of it will be (a) 0.30s (b) 0.32s (c) 0.33s (d) 0.35s The correct pption is 'c' can anyone explain?
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In a certain oscillatory system,the amplitude pf motion is 5m and the ...
Understanding the Oscillatory Motion
In this oscillatory system, we have the following parameters:
- Amplitude (A): 5 m
- Time Period (T): 4 s
The particle oscillates between the extremes of motion, which means it moves from -A to +A.
Finding the Angular Frequency
The angular frequency (ω) can be calculated using the relation:
- ω = 2π / T
Substituting the values:
- ω = 2π / 4 = π/2 rad/s
Position of the Particle
The displacement (x) from the mean position can be expressed as:
- x(t) = A * sin(ωt)
Finding Time Between Specific Points
We need to find the time taken for the particle to move from 4 m to 2 m on the same side of the center.
1. Position Calculation:
- For x = 4 m:
- 4 = 5 * sin(ωt1) → sin(ωt1) = 4/5
- For x = 2 m:
- 2 = 5 * sin(ωt2) → sin(ωt2) = 2/5
2. Time Calculation:
- Using the inverse sine function, we can calculate t1 and t2:
- t1 = (1/ω) * arcsin(4/5)
- t2 = (1/ω) * arcsin(2/5)
3. Time Difference:
- The time taken to move between these two positions is:
- Δt = t2 - t1
After performing the calculations, we find that Δt is approximately 0.33 s.
Conclusion
The time taken by the particle to pass between points at distances 4 m and 2 m from the center is 0.33 s, confirming that the correct option is (c).
In this oscillatory system, we have the following parameters:
- Amplitude (A): 5 m
- Time Period (T): 4 s
The particle oscillates between the extremes of motion, which means it moves from -A to +A.
Finding the Angular Frequency
The angular frequency (ω) can be calculated using the relation:
- ω = 2π / T
Substituting the values:
- ω = 2π / 4 = π/2 rad/s
Position of the Particle
The displacement (x) from the mean position can be expressed as:
- x(t) = A * sin(ωt)
Finding Time Between Specific Points
We need to find the time taken for the particle to move from 4 m to 2 m on the same side of the center.
1. Position Calculation:
- For x = 4 m:
- 4 = 5 * sin(ωt1) → sin(ωt1) = 4/5
- For x = 2 m:
- 2 = 5 * sin(ωt2) → sin(ωt2) = 2/5
2. Time Calculation:
- Using the inverse sine function, we can calculate t1 and t2:
- t1 = (1/ω) * arcsin(4/5)
- t2 = (1/ω) * arcsin(2/5)
3. Time Difference:
- The time taken to move between these two positions is:
- Δt = t2 - t1
After performing the calculations, we find that Δt is approximately 0.33 s.
Conclusion
The time taken by the particle to pass between points at distances 4 m and 2 m from the center is 0.33 s, confirming that the correct option is (c).
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In a certain oscillatory system,the amplitude pf motion is 5m and the ...
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In a certain oscillatory system,the amplitude pf motion is 5m and the time period is 4s.The time taken by the particle for passing between poits which are at distances of 4m and 2m from the center and on the same side of it will be (a) 0.30s (b) 0.32s (c) 0.33s (d) 0.35s The correct pption is 'c' can anyone explain?
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In a certain oscillatory system,the amplitude pf motion is 5m and the time period is 4s.The time taken by the particle for passing between poits which are at distances of 4m and 2m from the center and on the same side of it will be (a) 0.30s (b) 0.32s (c) 0.33s (d) 0.35s The correct pption is 'c' can anyone explain? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about In a certain oscillatory system,the amplitude pf motion is 5m and the time period is 4s.The time taken by the particle for passing between poits which are at distances of 4m and 2m from the center and on the same side of it will be (a) 0.30s (b) 0.32s (c) 0.33s (d) 0.35s The correct pption is 'c' can anyone explain? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a certain oscillatory system,the amplitude pf motion is 5m and the time period is 4s.The time taken by the particle for passing between poits which are at distances of 4m and 2m from the center and on the same side of it will be (a) 0.30s (b) 0.32s (c) 0.33s (d) 0.35s The correct pption is 'c' can anyone explain?.
In a certain oscillatory system,the amplitude pf motion is 5m and the time period is 4s.The time taken by the particle for passing between poits which are at distances of 4m and 2m from the center and on the same side of it will be (a) 0.30s (b) 0.32s (c) 0.33s (d) 0.35s The correct pption is 'c' can anyone explain? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about In a certain oscillatory system,the amplitude pf motion is 5m and the time period is 4s.The time taken by the particle for passing between poits which are at distances of 4m and 2m from the center and on the same side of it will be (a) 0.30s (b) 0.32s (c) 0.33s (d) 0.35s The correct pption is 'c' can anyone explain? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a certain oscillatory system,the amplitude pf motion is 5m and the time period is 4s.The time taken by the particle for passing between poits which are at distances of 4m and 2m from the center and on the same side of it will be (a) 0.30s (b) 0.32s (c) 0.33s (d) 0.35s The correct pption is 'c' can anyone explain?.
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In a certain oscillatory system,the amplitude pf motion is 5m and the time period is 4s.The time taken by the particle for passing between poits which are at distances of 4m and 2m from the center and on the same side of it will be (a) 0.30s (b) 0.32s (c) 0.33s (d) 0.35s The correct pption is 'c' can anyone explain?, a detailed solution for In a certain oscillatory system,the amplitude pf motion is 5m and the time period is 4s.The time taken by the particle for passing between poits which are at distances of 4m and 2m from the center and on the same side of it will be (a) 0.30s (b) 0.32s (c) 0.33s (d) 0.35s The correct pption is 'c' can anyone explain? has been provided alongside types of In a certain oscillatory system,the amplitude pf motion is 5m and the time period is 4s.The time taken by the particle for passing between poits which are at distances of 4m and 2m from the center and on the same side of it will be (a) 0.30s (b) 0.32s (c) 0.33s (d) 0.35s The correct pption is 'c' can anyone explain? theory, EduRev gives you an
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