A particle of mass $10\, gm$ moves in a field where potential energy per unit mas is given by expression $v = 8 \times 10^4\, x^2\, erg/gm$. If the total energy of the particle is $8 \times 10^7\, erg$ then the relation between $x$ and time $t$ is
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Potential energy per unit mass $=\frac{1}{2} \omega^{2} \mathrm{x}^{2}$
$8 \times 10^{4} x^{2}$ erg. $=\frac{1}{2} \omega^{2} x^{2}$
$\omega=400$
total energy $=\frac{1}{2} \mathrm{m} \omega^{2} \mathrm{A}^{2}$
$\therefore A=10 \mathrm{cm}$
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