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Which one of the following equations of motion represents simple harmonic motion? [2009]
where k, k0, k1 and a are all postive.
- a)Acceleration = – k(x + a)
- b)Acceleration = k(x + a)
- c)Acceleration = kx
- d)Acceleration = – k0x + k1x2
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Which one of the following equations of motion represents simple harmo...
a = – kX, X = x + a.
In simple harmonic motion acceleration is directly proportional to the displacement from the mean position. Also the acceleration is in the opposite direction of displacement.
In simple harmonic motion acceleration is directly proportional to the displacement from the mean position. Also the acceleration is in the opposite direction of displacement.
Most Upvoted Answer
Which one of the following equations of motion represents simple harmo...
Understanding Simple Harmonic Motion (SHM)
Simple Harmonic Motion is characterized by a restoring force that is directly proportional to the displacement from the equilibrium position and acts in the opposite direction. The general form of the equation for SHM can be expressed as:
- Acceleration (a) = -k * x
Here, "k" is a positive constant, and "x" represents the displacement from the equilibrium position.
Analysis of Given Options
Let’s evaluate the options provided:
a) Acceleration = – k(x + a)
- This can be rewritten as:
- Acceleration = -k * x - k * a
- The term "-k * x" denotes a restoring force, meeting the criteria for SHM. The constant "-k * a" simply shifts the equilibrium position but does not alter the nature of the motion. Thus, this option represents SHM.
b) Acceleration = k(x + a)
- Here, acceleration is positively related to displacement. This means the force acts in the same direction as displacement, which is not characteristic of SHM.
c) Acceleration = kx
- Similar to option b, here the acceleration is also directly proportional to displacement but in a positive direction. This can lead to unbounded motion, not SHM.
d) Acceleration = – k0x + k1x²
- This equation includes a quadratic term (k1x²). The presence of this non-linear term means the restoring force is not solely dependent on displacement, thus not representing SHM.
Conclusion
The correct answer is option a because it meets the defining criteria of simple harmonic motion: the acceleration is proportional to displacement and directed towards the equilibrium position.
Simple Harmonic Motion is characterized by a restoring force that is directly proportional to the displacement from the equilibrium position and acts in the opposite direction. The general form of the equation for SHM can be expressed as:
- Acceleration (a) = -k * x
Here, "k" is a positive constant, and "x" represents the displacement from the equilibrium position.
Analysis of Given Options
Let’s evaluate the options provided:
a) Acceleration = – k(x + a)
- This can be rewritten as:
- Acceleration = -k * x - k * a
- The term "-k * x" denotes a restoring force, meeting the criteria for SHM. The constant "-k * a" simply shifts the equilibrium position but does not alter the nature of the motion. Thus, this option represents SHM.
b) Acceleration = k(x + a)
- Here, acceleration is positively related to displacement. This means the force acts in the same direction as displacement, which is not characteristic of SHM.
c) Acceleration = kx
- Similar to option b, here the acceleration is also directly proportional to displacement but in a positive direction. This can lead to unbounded motion, not SHM.
d) Acceleration = – k0x + k1x²
- This equation includes a quadratic term (k1x²). The presence of this non-linear term means the restoring force is not solely dependent on displacement, thus not representing SHM.
Conclusion
The correct answer is option a because it meets the defining criteria of simple harmonic motion: the acceleration is proportional to displacement and directed towards the equilibrium position.
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Which one of the following equations of motion represents simple harmonic motion? [2009]where k, k0, k1 and a are all postive.a)Acceleration = – k(x + a)b)Acceleration = k(x + a)c)Acceleration = kxd)Acceleration = – k0x + k1x2Correct answer is option 'A'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Which one of the following equations of motion represents simple harmonic motion? [2009]where k, k0, k1 and a are all postive.a)Acceleration = – k(x + a)b)Acceleration = k(x + a)c)Acceleration = kxd)Acceleration = – k0x + k1x2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following equations of motion represents simple harmonic motion? [2009]where k, k0, k1 and a are all postive.a)Acceleration = – k(x + a)b)Acceleration = k(x + a)c)Acceleration = kxd)Acceleration = – k0x + k1x2Correct answer is option 'A'. Can you explain this answer?.
Which one of the following equations of motion represents simple harmonic motion? [2009]where k, k0, k1 and a are all postive.a)Acceleration = – k(x + a)b)Acceleration = k(x + a)c)Acceleration = kxd)Acceleration = – k0x + k1x2Correct answer is option 'A'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Which one of the following equations of motion represents simple harmonic motion? [2009]where k, k0, k1 and a are all postive.a)Acceleration = – k(x + a)b)Acceleration = k(x + a)c)Acceleration = kxd)Acceleration = – k0x + k1x2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following equations of motion represents simple harmonic motion? [2009]where k, k0, k1 and a are all postive.a)Acceleration = – k(x + a)b)Acceleration = k(x + a)c)Acceleration = kxd)Acceleration = – k0x + k1x2Correct answer is option 'A'. Can you explain this answer?.
Solutions for Which one of the following equations of motion represents simple harmonic motion? [2009]where k, k0, k1 and a are all postive.a)Acceleration = – k(x + a)b)Acceleration = k(x + a)c)Acceleration = kxd)Acceleration = – k0x + k1x2Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET.
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