Question

A body of mass m is situated in a potential field U(x) = U0(1-cos αx ) when U0 and α are constants. Find the time period of small oscillations​

Answer 1

The time period of small oscillations can be represented as :

• As per the question, U(x) = U₀(1-cos αx )

• Differentiating both sides by d(x):

F= $\frac{-dU}{dx}=\frac{-d(U0-U0cos ax )}{dx}$

= -U₀αsinαx

= -U₀ααx ( for small αx , sinαx ≈ αx)

= -U₀α²x

• As we know , F = -kx

• so, k= U₀α²

• Therefore, Time period (T) = $2\pi \sqrt{\frac{m}{Uo a^{2} } }$

Answer 2

Answer:

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