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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$1.$ The phase space diagram for a ball thrown vertically up from ground is
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$2.$ The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and $E_1$ and $E_2$ are the total mechanical energies respectively. Then $Image$
$(A)$ $ E_1=\sqrt{2} E_2$ $(B)$ $ E_1=2 E_2$
$(C)$ $ E_1=4 E_2$ $(D)$ $ E_1=16 E_2$
$3.$ Consider the spring-mass system, with the mass submerged in water, as shown in the figure. The phase space diagram for one cycle of this system is $Image$
mcq $Image$
Give the answer question $1,2$ and $3.$
