A particle of mass m in a unidirectional potential field have potential energy U(x)=α+2 β x2, where α and β are positive constants. Find its time period of oscillation.

Question

A particle of mass m in a unidirectional potential field have potential energy U(x)=α+2 β x2, where α and β are positive constants. Find its time period of oscillation. (A) 2 π √(2 β/m) (B) 2 π √(m/2 β) (C) π √(m/β) (D) π √(β/m)

Tardigrade Admin · Accepted Answer

U(x)=α+2 β x2 F=-(d U(x)/d x) F=-4 β x T=2 π √(m/k) T=2 π √(m/4 β) cos [k=β] T=√[π](m/β)

Q. A particle of mass $m$ in a unidirectional potential field have potential energy $U (x) = α + 2 β x^{2}$ , where $α$ and $β$ are positive constants. Find its time period of oscillation.

$2 π \frac{2 β}{m}$

$2 π \frac{m}{2 β}$

$π \frac{m}{β}$

$π \frac{β}{m}$

$U (x) = α + 2 β x^{2}$
$F = - \frac{d U ( x )}{d x}$
$F = - 4 β x$
$T = 2 π \frac{m}{k}$
$T = 2 π \frac{m}{4 β} cos [k = β]$
$T = π \frac{m}{β}$

Q. A particle of mass m in a unidirectional potential field have potential energy U(x)=α+2βx2, where α and β are positive constants. Find its time period of oscillation.

2πm2β​​

2π2βm​​

πβm​​

πmβ​​