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A particle of mass m is located in a one...

A particle of mass m is located in a one dimensional potential field where potential energy of the particle has the form u(x) = `a/x^(2)-b/x)`, where a and b are positive constants. Find the period of small oscillations of the particle.

Answer

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A partical of mass m is located in a unidimensionnal potential field where potentical energy of the partical depends on the coordinates x as U (x) = (A)/(x^(2)) - (B)/(x) where A and B are positive constant. Find the time period of small oscillation that the partical perform about equilibrium possition.

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Knowledge Check

  • A particle of mass m is located in a one dimensional potential field where potential energy of the particle has the form U (x) = (a)/(x^(2)) - (b)/(x) where a and b are positive constants. The position of equilibrium is:

    A
    `(b)/(2a)`
    B
    `(2b)/(a)`
    C
    `(a)/(b)`
    D
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  • 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 constants. The period of small oscillations of the particle is

    A
    `2pi sqrt(m/(Ap))`
    B
    `2pi sqrt(m/(Ap^(2)))`
    C
    `2pi sqrt(m/A)`
    D
    `1/(2pi) sqrt((Ap)/m)`

  • 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
    `2pi sqrt (( m )/((Ap )))`
    B
    `2pi sqrt (( m )/(( A p ^(2))))`
    C
    `2pi sqrt ((m)/( (A)))`
    D
    `(1)/(2pi) sqrt ((Ap)/(m))`

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    A partical of mass m is located in a unidimensionnal potential field where potentical energy of the partical depends on the coordinates x as: U (x) = U_(0) (1 - cos Ax), U_(0) and A constants. Find the period of small oscillation that the partical performs about the equilibrium position.

    Solve the foregoing problem if the potential energy has the form U(x)=a//x^(2)-b//x, , where a and b are positive constants.

    A particle located in one dimensional potential field has potential energy function U(x)=(a)/(x^(2))-(b)/(x^(3)) , where a and b are positive constants. The position of equilibrium corresponds to x equal to

    A particle located in a one-dimensional potential field has its potential energy function as U(x)=(a)/(x^4)-(b)/(x^2) , where a and b are positive constants. The position of equilibrium x corresponds to

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

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