A particle of mass m is located in a one dimensional potential field where potential energy is given by: V(.x.)=A(.1- cos px.), Where A and p are constant. The period of small oscillations of the particle is :-

Question

A particle of mass m is located in a one dimensional potential field where potential energy is given by: V(.x.)=A(.1- cos px.), Where A and p are constant. The period of small oscillations of the particle is :- (A) 2π √(m/(. A p .)) (B) 2π √(m/(A p2)) (C) 2π √(m/(. A .)) (D) (1/2 π )√(A p/m)

Tardigrade Admin · Accepted Answer

V=A(.1- cos px.) F=-(d V/d x)=-Ap sin px For small displacement sin px=px ∴ F=-Ap2x T=2π √(m/K)=2π √(m/A p2)

Q. A particle of mass $m$ is located in a one dimensional potential field where potential energy is given by : $V (x) = A (1 - cos p x),$ Where $A$ and $p$ are constant. The period of small oscillations of the particle is :-

$2 π \frac{m}{( A p )}$

$2 π \frac{m}{( A p ^{2} )}$

$2 π \frac{m}{( A )}$

$\frac{1}{2 π} \frac{A p}{m}$

$V = A (1 - cos p x)$
$F = - \frac{d V}{d x} = - A p sin p x$
For small displacement
$sin p x = p x$
$∴ F = - A p^{2} x$
$T = 2 π \frac{m}{K} = 2 π \frac{m}{A p ^{2}}$

Q. A particle of mass m is located in a one dimensional potential field where potential energy is given by : V(x)=A(1−cospx), Where A and p are constant. The period of small oscillations of the particle is :-

2π(Ap)m​​

2π(Ap2)m​​

2π(A)m​​

2π1​mAp​​