A particle is oscillating in a straight line about a centre of force \( O \), towards which when...

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A particle is oscillating in a straight line about a centre of force \( O \), towards which when at a distance \( x \) the force is \( m n^{2} x \) where \( m \) is the mass, \( n \) a constant. The amplitude is \( a=15 \mathrm{~cm} \). When at a distance \( a \sqrt{3} / 2 \) from \( O \) the particle receives a blow in the direction of motion which generates extra velocity na. If the velocity is away from \( O \), find the new amplitude. What is the answer if the velocity of block was towards origin.
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