A particle of mass m is moving along the x-direction due to the action of potential energy which is given by V(x)= -Ax*e-kx. Due to this the particle is found to oscillate. What is the time period of this oscillation??

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Dear student
U=-Axe-kxF=-dUdxF=-d(-Axe-kx)dxF=Ad(xe-kx)dxF=A(-Kxe-kx+e-kx×1)F=A(-Kx+1)e-kxF=A(-Kx+1)(1-kx1)  ( neglecting higher powers of x)F=A(-Kx+1)(1-Kx) =A(1-2kx+K2x2)F=A(1-2kx)  (neglecting x2 term as x is small)F=-A(2kx-1)=-(2AK)(x-12K)a=-(2AK)m(x-12K)comparing with standard eqn of shm ω2=(2AK)mω=(2AK)m2πT=(2AK)mT=2πm(2AK)Regards

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