If a body is executing simple harmonic motion and its current displacement is √3/2 times the amplitude from its mean position, then the ratio between potential energy and kinetic energy is
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Displacement of the body from mean position = √3/2*A
where A is the amplitude of the oscillation suppose.
So,
By formula,
Potential energy = 1/2*k*x^2
Kinetic energy = 1/2*k*(A^2-x^2)
So,
Potential energy / Kinetic Energy
= x^2/(A^2-x^2) = 3/4*A^2/A^2-3/4A^2 = 3/4A^2 / 1/4A^2 = 3:1
where A is the amplitude of the oscillation suppose.
So,
By formula,
Potential energy = 1/2*k*x^2
Kinetic energy = 1/2*k*(A^2-x^2)
So,
Potential energy / Kinetic Energy
= x^2/(A^2-x^2) = 3/4*A^2/A^2-3/4A^2 = 3/4A^2 / 1/4A^2 = 3:1
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