Question

A particle of mass $m$ m in a unidirectional potential field has potential energy $U\left(\right.x\left.\right)=a+2bx^{2}$ where a and b are positive constants. Find time period of oscillation:-

• A. $2\pi \sqrt{\frac{2 b}{ m}}$
• B. $2\pi \sqrt{\frac{m}{2 b}}$
• C. $\pi \sqrt{\frac{m}{b}}$
• D. $\pi \sqrt{\frac{b}{m}}$

Answer 1

Answer: (C)

$F=-\sqrt[]{\frac{d U}{d x}}$
$F=-4bx\Rightarrow K=4b$
$T=2\pi \sqrt{\frac{m}{4 b}}=\pi \sqrt{\frac{m}{b}}$