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If a block is placed on platform executing S.H.M along the vertical, then for the block and platform to remain together the maximum amplitude is rmax=g/4×pi^2×v^2 where v is frequency of S.H.M someone plz prove me the above formula?
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Proof of the formula for maximum amplitude in SHM
Concept:
In simple harmonic motion (SHM), the maximum amplitude of oscillation is determined by the equilibrium position, gravitational acceleration, and frequency of oscillation.
Formula:
The formula for maximum amplitude (rmax) in SHM is given by:
rmax = g / (4 * π^2 * v^2)
Derivation:
- Let's consider a block placed on a platform executing SHM along the vertical direction.
- For the block and platform to remain together, the maximum amplitude should be such that the gravitational force acting downwards is balanced by the maximum restoring force of the SHM motion.
Equilibrium Condition:
At the maximum amplitude, the gravitational force (mg) is balanced by the maximum restoring force (k * rmax), where k is the spring constant.
Equating Forces:
mg = k * rmax
m * g = m * (4 * π^2 * v^2) * rmax
Solving for rmax:
rmax = g / (4 * π^2 * v^2)
Conclusion:
The formula for maximum amplitude in SHM is derived by equating the gravitational force to the maximum restoring force at the equilibrium position. This formula helps in determining the maximum displacement of the block during oscillation.
Concept:
In simple harmonic motion (SHM), the maximum amplitude of oscillation is determined by the equilibrium position, gravitational acceleration, and frequency of oscillation.
Formula:
The formula for maximum amplitude (rmax) in SHM is given by:
rmax = g / (4 * π^2 * v^2)
Derivation:
- Let's consider a block placed on a platform executing SHM along the vertical direction.
- For the block and platform to remain together, the maximum amplitude should be such that the gravitational force acting downwards is balanced by the maximum restoring force of the SHM motion.
Equilibrium Condition:
At the maximum amplitude, the gravitational force (mg) is balanced by the maximum restoring force (k * rmax), where k is the spring constant.
Equating Forces:
mg = k * rmax
m * g = m * (4 * π^2 * v^2) * rmax
Solving for rmax:
rmax = g / (4 * π^2 * v^2)
Conclusion:
The formula for maximum amplitude in SHM is derived by equating the gravitational force to the maximum restoring force at the equilibrium position. This formula helps in determining the maximum displacement of the block during oscillation.
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If a block is placed on platform executing S.H.M along the vertical, then for the block and platform to remain together the maximum amplitude is rmax=g/4×pi^2×v^2 where v is frequency of S.H.M someone plz prove me the above formula?
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If a block is placed on platform executing S.H.M along the vertical, then for the block and platform to remain together the maximum amplitude is rmax=g/4×pi^2×v^2 where v is frequency of S.H.M someone plz prove me the above formula? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If a block is placed on platform executing S.H.M along the vertical, then for the block and platform to remain together the maximum amplitude is rmax=g/4×pi^2×v^2 where v is frequency of S.H.M someone plz prove me the above formula? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a block is placed on platform executing S.H.M along the vertical, then for the block and platform to remain together the maximum amplitude is rmax=g/4×pi^2×v^2 where v is frequency of S.H.M someone plz prove me the above formula?.
If a block is placed on platform executing S.H.M along the vertical, then for the block and platform to remain together the maximum amplitude is rmax=g/4×pi^2×v^2 where v is frequency of S.H.M someone plz prove me the above formula? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If a block is placed on platform executing S.H.M along the vertical, then for the block and platform to remain together the maximum amplitude is rmax=g/4×pi^2×v^2 where v is frequency of S.H.M someone plz prove me the above formula? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a block is placed on platform executing S.H.M along the vertical, then for the block and platform to remain together the maximum amplitude is rmax=g/4×pi^2×v^2 where v is frequency of S.H.M someone plz prove me the above formula?.
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