The potential energy of a particle executing SHM alon x-axis is U=U0(1-cosax).What is the frequency of oscillation?

Dear student

U=U0(1-cosax)

Force=-dU/dx=-aU0sinax=-w^2 (x)

from here you can easliy calculate frequency on comparing the two..

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Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi

U = U₀(1-cosax)

F = -dU/dx = -U_oasinax

for small x , sinax is small or sinax = ax

F = -U₀a²x

a = -U_oa²x/m                              (a = -w²x)

-w²x = -U_oa²x/m

 w = (U_oa²/m)^1/2

U = U0(1-cosax) F = -dU/dx = -Uoasinax for small x , sinax is small or sinax = ax F = -U0a2x a = -Uoa2x/m (a = -w2x) -w2x = -Uoa2x/m w = (Uoa2/m)1/2