if t = as²+ bsthen acceleration of particle is:proportional to vproportional to v²proportional to v³independent of v

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A particle of mass m is executing oscillations about the origin on the x axis. Its potential energy is V(x) = k | x |3 where k is a positive constant. If the amplitude of oscillation is a, then its time period T is

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A particle of mass m is executing oscillations about the origin on x axis. its potential energy is U (x) = k|x|^3, where k is constant. If the amplitude of oscillation is a then it's time period T is?? proportional to 1/root a independent of a proportional to root a proportional to a^3/2 PLZZ SOMEONE ANSWER THIS QUESTION.

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When a particle of mass m moves on the x-axis in a potential of the form V(x) = kx2 it performs simple harmonic motion. Thecorresponding time period is proportional to as can be seen easily using dimensional analysis. However, the motion of a particle can be periodic even when its potential energy increases on both sides of x = 0 in a way different from kx2 and its total energy is such that the particle does not escape to infinity. Consider a particle of mass m moving on the x-axis. Its potential energy is V(x) = αx4 (α > 0) for |x| near the origin and becomes a constant equal to V0 for |x| > X0 (see figur e).Q.The acceleration of this particle for |x| > X0 is

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Paragraph for Questions 16to 18When a particle of mass m moves on the x-axis in a potentialof the form V(x) = kx2 it performs simple harmonic motion.The corresponding time period is proportional to , as canbe seen easily using dimensional analysis. However, themotion of a particle can be periodic even when its potentialenergy increases on both sides of x = 0 in a way differentfrom kx2 and its total energy is such that the particle does notescape to infinity. Consider a particle of mass m moving onthe x-axis. Its potential energy is V(x) = αx4 (α > 0) for |x|near the origin and becomes a constant equal to V0 for|x| ≥ X0 (see figur e).Q.The acceleration of this particle for |x| > X0 is

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A particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance r. The speed of the particle is

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if t = as²+ bsthen acceleration of particle is:proportional to vproportional to v²proportional to v³independent of v

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