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The maximum velocity of a particle executing SHM with an amplitude 7mm, is 4.4m/s. Calculate the period of oscillation- A)0.1 sec B)100sec C)0.01sec D)10 sec?
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The maximum velocity of a particle executing SHM with an amplitude 7mm...
Understanding SHM (Simple Harmonic Motion)
Simple Harmonic Motion (SHM) is characterized by oscillatory motion where a particle moves back and forth around an equilibrium position. The motion can be described using parameters like amplitude, maximum velocity, and period.
Given Data
- Amplitude (A) = 7 mm = 0.007 m
- Maximum Velocity (V_max) = 4.4 m/s
Key Formula
The maximum velocity in SHM can be expressed as:
V_max = A * ω
Where:
- V_max = Maximum velocity
- A = Amplitude
- ω = Angular frequency
The angular frequency ω is related to the period (T) of the motion:
ω = 2π / T
Calculate Angular Frequency
Rearranging the maximum velocity formula to solve for ω gives:
ω = V_max / A
Substituting the values:
ω = 4.4 m/s / 0.007 m = 628.57 rad/s
Calculate the Period
Now, using the relationship between angular frequency and period:
T = 2π / ω
Substituting the value of ω:
T = 2π / 628.57 ≈ 0.01 sec
Conclusion
The period of oscillation is approximately 0.01 seconds.
Final Answer
The correct option is C) 0.01 sec.
Simple Harmonic Motion (SHM) is characterized by oscillatory motion where a particle moves back and forth around an equilibrium position. The motion can be described using parameters like amplitude, maximum velocity, and period.
Given Data
- Amplitude (A) = 7 mm = 0.007 m
- Maximum Velocity (V_max) = 4.4 m/s
Key Formula
The maximum velocity in SHM can be expressed as:
V_max = A * ω
Where:
- V_max = Maximum velocity
- A = Amplitude
- ω = Angular frequency
The angular frequency ω is related to the period (T) of the motion:
ω = 2π / T
Calculate Angular Frequency
Rearranging the maximum velocity formula to solve for ω gives:
ω = V_max / A
Substituting the values:
ω = 4.4 m/s / 0.007 m = 628.57 rad/s
Calculate the Period
Now, using the relationship between angular frequency and period:
T = 2π / ω
Substituting the value of ω:
T = 2π / 628.57 ≈ 0.01 sec
Conclusion
The period of oscillation is approximately 0.01 seconds.
Final Answer
The correct option is C) 0.01 sec.
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The maximum velocity of a particle executing SHM with an amplitude 7mm, is 4.4m/s. Calculate the period of oscillation- A)0.1 sec B)100sec C)0.01sec D)10 sec?
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The maximum velocity of a particle executing SHM with an amplitude 7mm, is 4.4m/s. Calculate the period of oscillation- A)0.1 sec B)100sec C)0.01sec D)10 sec? 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 The maximum velocity of a particle executing SHM with an amplitude 7mm, is 4.4m/s. Calculate the period of oscillation- A)0.1 sec B)100sec C)0.01sec D)10 sec? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The maximum velocity of a particle executing SHM with an amplitude 7mm, is 4.4m/s. Calculate the period of oscillation- A)0.1 sec B)100sec C)0.01sec D)10 sec?.
The maximum velocity of a particle executing SHM with an amplitude 7mm, is 4.4m/s. Calculate the period of oscillation- A)0.1 sec B)100sec C)0.01sec D)10 sec? 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 The maximum velocity of a particle executing SHM with an amplitude 7mm, is 4.4m/s. Calculate the period of oscillation- A)0.1 sec B)100sec C)0.01sec D)10 sec? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The maximum velocity of a particle executing SHM with an amplitude 7mm, is 4.4m/s. Calculate the period of oscillation- A)0.1 sec B)100sec C)0.01sec D)10 sec?.
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