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Setler [38]
3 years ago
11

A particle of unit mass moves in a potential V(x)= ax^2+b/x^2 . Where a and b are constnts. Calcuate the angular frequency of sm

all oscillations about the minimum of potential.
Physics
1 answer:
Sholpan [36]3 years ago
4 0

Answer:

Explanation:

Given

Potential Energy is given by

U(x)=ax^2+\frac{b}{x^2}

And Force is given by

F=-\frac{\mathrm{d} U}{\mathrm{d} x}

Particle will be at equilibrium when Potential Energy is either minimum or maximum

F=-\left ( 2ax-\frac{2b}{x^3}\right )

i.e.ax=\frac{b}{x^3}

x_0=(\frac{b}{a})^{0.25}

So angular Frequency of small oscillation is given by

\omega =\sqrt{\frac{U''(x)}{m}}

for m=1

we get    \omega =\sqrt{\frac{U''(x_0)}{1}}

U''(x_0)=2a+6a= 8a

\omega =\sqrt{8a}

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