A particle of mass m m in a unidirectional potential field has potential energy U(.x.)=a+2bx2 where a and b are positive constants. Find time period of oscillation:-

Question

A particle of mass m m in a unidirectional potential field has potential energy U(.x.)=a+2bx2 where a and b are positive constants. Find time period of oscillation:- (A) 2π √(2 b/ m) (B) 2π √(m/2 b) (C) π √(m/b) (D) π √(b/m)

Tardigrade Admin · Accepted Answer

F=-√[](d U/d x) F=-4bx⇒ K=4b T=2π √(m/4 b)=π √(m/b)

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

$2 π \frac{2 b}{m}$

$2 π \frac{m}{2 b}$

$π \frac{m}{b}$

$π \frac{b}{m}$

$F = - \frac{d U}{d x}$
$F = - 4 b x \Rightarrow K = 4 b$
$T = 2 π \frac{m}{4 b} = π \frac{m}{b}$

Q. A particle of mass m m in a unidirectional potential field has potential energy U(x)=a+2bx2 where a and b are positive constants. Find time period of oscillation:-

2πm2b​​

2π2bm​​

πbm​​

πmb​​