IIT JEE Mains and Advanced PYQ: Simple Harmonic Motion (SHM) #neet #jeemain #jeeadvance #physics#pyq

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. The corresponding time period is proportional to √𝒎/ 𝒌, 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) = 𝒂𝒙4 (𝜶 greater then 𝟎) for |𝒙| near the origin and becomes a constant equal to 𝑽0 for |𝒙|≥ 𝑿0 (see figure).

(2010 Adv.)

IIT JEE Mains and Advanced PYQ: Simple Harmonic Motion (SHM) #neet #jeemain #jeeadvance #physics#pyq

[Zyddddddiii]

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