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A particle executing S.H.M of amplitude 4 cm and T = 4 sec. The time taken (in sec) by it to move from positive extreme position to half the amplitude is :
Correct answer is between '0.665,0.669'. Can you explain this answer?
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A particle executing S.H.M of amplitude 4 cm and T= 4 sec. The time ta...
The correct answer is: 0.667
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A particle executing S.H.M of amplitude 4 cm and T= 4 sec. The time ta...
Given:
Amplitude (A) = 4 cm
Time period (T) = 4 sec
To find:
Time taken by the particle to move from positive extreme position to half the amplitude
Formula:
The equation for Simple Harmonic Motion (SHM) is given by:
y = A * sin (2πt / T)
Where:
y = displacement of the particle at any given time t
A = amplitude of the motion
t = time
T = time period
Explanation:
To find the time taken by the particle to move from the positive extreme position to half the amplitude, we need to find the time when the displacement is half the amplitude.
Let's consider the equation for SHM:
y = A * sin (2πt / T)
We know that the displacement at the positive extreme position is equal to the amplitude (A).
So, when y = A/2, we can solve the equation to find the corresponding time (t).
Calculation:
Given:
A = 4 cm
T = 4 sec
Substituting the values in the equation:
A/2 = 4/2 = 2 cm
y = A * sin (2πt / T)
2 = 4 * sin (2πt / 4)
Dividing by 4:
1/2 = sin (2πt / 4)
Taking inverse sine of both sides:
sin^(-1)(1/2) = 2πt / 4
Using the inverse sine function, we find that sin^(-1)(1/2) = π/6
π/6 = 2πt / 4
Simplifying the equation:
1/6 = t/4
Cross multiplying:
4 = 6t
Solving for t:
t = 4/6 = 2/3 ≈ 0.667 sec
Therefore, the time taken by the particle to move from the positive extreme position to half the amplitude is approximately 0.667 seconds.
Amplitude (A) = 4 cm
Time period (T) = 4 sec
To find:
Time taken by the particle to move from positive extreme position to half the amplitude
Formula:
The equation for Simple Harmonic Motion (SHM) is given by:
y = A * sin (2πt / T)
Where:
y = displacement of the particle at any given time t
A = amplitude of the motion
t = time
T = time period
Explanation:
To find the time taken by the particle to move from the positive extreme position to half the amplitude, we need to find the time when the displacement is half the amplitude.
Let's consider the equation for SHM:
y = A * sin (2πt / T)
We know that the displacement at the positive extreme position is equal to the amplitude (A).
So, when y = A/2, we can solve the equation to find the corresponding time (t).
Calculation:
Given:
A = 4 cm
T = 4 sec
Substituting the values in the equation:
A/2 = 4/2 = 2 cm
y = A * sin (2πt / T)
2 = 4 * sin (2πt / 4)
Dividing by 4:
1/2 = sin (2πt / 4)
Taking inverse sine of both sides:
sin^(-1)(1/2) = 2πt / 4
Using the inverse sine function, we find that sin^(-1)(1/2) = π/6
π/6 = 2πt / 4
Simplifying the equation:
1/6 = t/4
Cross multiplying:
4 = 6t
Solving for t:
t = 4/6 = 2/3 ≈ 0.667 sec
Therefore, the time taken by the particle to move from the positive extreme position to half the amplitude is approximately 0.667 seconds.
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A particle executing S.H.M of amplitude 4 cm and T= 4 sec. The time taken (in sec) by it to move from positive extreme position to half the amplitude is :Correct answer is between '0.665,0.669'. Can you explain this answer?
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A particle executing S.H.M of amplitude 4 cm and T= 4 sec. The time taken (in sec) by it to move from positive extreme position to half the amplitude is :Correct answer is between '0.665,0.669'. 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 executing S.H.M of amplitude 4 cm and T= 4 sec. The time taken (in sec) by it to move from positive extreme position to half the amplitude is :Correct answer is between '0.665,0.669'. 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 executing S.H.M of amplitude 4 cm and T= 4 sec. The time taken (in sec) by it to move from positive extreme position to half the amplitude is :Correct answer is between '0.665,0.669'. Can you explain this answer?.
A particle executing S.H.M of amplitude 4 cm and T= 4 sec. The time taken (in sec) by it to move from positive extreme position to half the amplitude is :Correct answer is between '0.665,0.669'. 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 executing S.H.M of amplitude 4 cm and T= 4 sec. The time taken (in sec) by it to move from positive extreme position to half the amplitude is :Correct answer is between '0.665,0.669'. 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 executing S.H.M of amplitude 4 cm and T= 4 sec. The time taken (in sec) by it to move from positive extreme position to half the amplitude is :Correct answer is between '0.665,0.669'. Can you explain this answer?.
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