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Discuss S.H.M as a special case of circular motion and derive the expression for displacement, velocity and acceleration of a body executing S.H.M?
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Discuss S.H.M as a special case of circular motion and derive the expr...
Special case of circular motion:
- Simple Harmonic Motion (S.H.M) can be considered as a special case of circular motion where the projection of a point moving uniformly around the circumference of a circle onto a diameter creates S.H.M.
Expression for displacement, velocity, and acceleration:
- The displacement of a body undergoing S.H.M can be represented as:
\[ x = A \sin(\omega t + \phi) \]
where x is the displacement, A is the amplitude, ω is the angular frequency, t is the time, and φ is the phase constant.
- The velocity of the body can be expressed as:
\[ v = A \omega \cos(\omega t + \phi) \]
where v is the velocity.
- The acceleration of the body is given by:
\[ a = -A \omega^2 \sin(\omega t + \phi) \]
where a is the acceleration.
- In S.H.M, the displacement and acceleration are out of phase by 90 degrees, while velocity and displacement are in phase.
- The maximum values of velocity and acceleration occur when the displacement is zero, and the maximum displacement occurs when the velocity is zero.
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Discuss S.H.M as a special case of circular motion and derive the expression for displacement, velocity and acceleration of a body executing S.H.M?
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Discuss S.H.M as a special case of circular motion and derive the expression for displacement, velocity and acceleration of a body executing S.H.M? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Discuss S.H.M as a special case of circular motion and derive the expression for displacement, velocity and acceleration of a body executing S.H.M? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Discuss S.H.M as a special case of circular motion and derive the expression for displacement, velocity and acceleration of a body executing S.H.M?.
Discuss S.H.M as a special case of circular motion and derive the expression for displacement, velocity and acceleration of a body executing S.H.M? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Discuss S.H.M as a special case of circular motion and derive the expression for displacement, velocity and acceleration of a body executing S.H.M? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Discuss S.H.M as a special case of circular motion and derive the expression for displacement, velocity and acceleration of a body executing S.H.M?.
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