InterviewSolution
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InterviewSolution
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A body of mass m is situated in a potential field U(x) = Uo(1 – cos α x) when Uo and α are constants. Find the time period of small oscillations. |
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Answer» U(x) = Uo(1 − cos αx) Differentiating both sides with respect to x \(\frac{dU(x)}{dx}\)= Uo[0 + α sin αx ] = Uoα sin αx ∴ F = − \(\frac{dU(x)}{dx}\) = −Uoα sin α x When oscillations are small, sin θ ≈ θ or sin αx = αx ∴ F = −Uoα(αx) = −Uoα2x ∴ F = −(Uoα2) (i) We know that F = −kx (ii) k = Uoα2 {From (i) & (ii)} ∴ T = \(2\pi\sqrt{\frac{m}{k}}=2\pi\sqrt{\frac{m}{U_o\alpha^2}}\) |
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