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A particle of mass \( 10 \mathrm{gm} \) moves in a field where potential energy per unit mass is given by expression \( U=8 \times 10^{4} x^{2} \mathrm{erg} / \mathrm{gm} \). If the total energy of the particle is \( 8 \times 10^{7} \) erg then the relation between \( x \) and time \( t \) is :
(A) \( x=10 \sin (400 t+\phi) \mathrm{cm} \quad \) (B) \( x=\sin (400 t+\phi) \mathrm{m} \)
(C) \( x=10 \sin (40 t+\phi) \mathrm{cm} \)
(D) \( x=100 \sin (4 t+\phi) \mathrm{m} \)
\( [\phi= \) constant \( ] \)
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