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.

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Payal Gupta | Contributor-Level 10

7 months ago

This is a short answer type question as classified in NCERT Exemplar

given potential energy associated with the field

U (x)=U_o (1-cos $α x$ )

F=-dU (x)/dx

F=-d (U_o-U_ocos $α x$ )=-U_o $α$ sin $α x$

F=-U_{o $α^{2} x$}

F $\propto - x$

Motion is SHM for small oscillatons

F=-mw²X

Mw²=U_{o $α^{2}$}

w²= $\frac{U_{o} α^{2}}{m}$ , w= $\sqrt[]{\frac{U_{o} α^{2}}{m}}$

T= $\frac{2 π}{w}$ = $2 π \sqrt[]{\frac{m}{U_{o} α^{2}}}$

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