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A particle of mass m is located in a one dimensional potential field where potential energy is given by V(x) = A(1 - cospx), where A and p are constants. The period of small oscillations of the particle is |
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Answer» `2pi sqrt(m/(AP))` Force, `F =-(dV)/(dt) =-d/(dx) (A-A cos px) =-Ap sinpx` For small x, `F =-Ap^(2)x` Acceleration, `a=F/m =-(Ap^(2)x)/m`.............(i) The standard equation of SHM is, `a=-omega^(2)x`...........(II) Comparing (i) and (ii), we get `omega^(2) =(Ap^(2))/m` or `omega =sqrt((Ap^(2))/m)` Periodic of OSCILLATION, `T =(2pi)/omega =2pisqrt(m/(Ap^(2))` |
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