Home
Class 12
PHYSICS
A particle of mass 3 kg moves in aone di...

A particle of mass 3 kg moves in aone dimensional field along x-axis. The force due to the field depends on its position as `F= 729 x^(6) - 64` . Find the state equilibrium position. Determine the time period of osciallations for small amplitude osciallations about the stable equlibrium position.

Text Solution

AI Generated Solution

To solve the problem step by step, we will follow the necessary physics principles and calculations. ### Step 1: Determine the Equilibrium Position The equilibrium position is found when the net force acting on the particle is zero. The force is given by: \[ F = 729x^6 - 64 \] To find the equilibrium position, we set the force equal to zero: ...
Promotional Banner

Topper's Solved these Questions

  • OSCILLATIONS

    AAKASH INSTITUTE ENGLISH|Exercise EXAMPLE|21 Videos

  • OSCILLATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Exercise|18 Videos

  • OSCILLATIONS

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT ( SECTION-I(SUBJECTIVE TYPE QUESTIONS) )|7 Videos

  • NUCLEI

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT (SECTION-D)|10 Videos

  • PHYSICAL WORLD

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT (Section-B)|4 Videos

Similar Questions

Explore conceptually related problems

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.

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.

A particle of mass 2 kg moves in simple harmonic motion and its potential energy U varies with position x as shown. The period of oscillation of the particle is

A particle of mass 2 kg moves in simple harmonic motion and its potential energy U varies with position x as shown. The period of oscillation of the particle is

A particle of mass 1 kg is moving along x - axis and a force F is also acting along x -axis in such a way that its displacement is varying as : x=3t^(2) . Find work done by force F when it will move 2m.

Force acting on a particle constrained to move along x-axis is F=(x-4) . Here, F is in newton and x in metre. Find the equilibrium position and state whether it is stable or unstable equilibrium.

A particle moving with S.H.M. has velocitiesof 4 cm//s and 3 cm//s at distances of 3 cm and 4 cm respectively from the equilibrium position. Find (a)The amplitude of the osciallation (b) Time period (c ) The velocity of the particle as is pases through the equilibrium position.

A particle is moving along x-axis under the action of force, F which varies with its position as F prop(1)/(4sqrtx). Find the variation of power due to this fore with x.

The potential energy U(x) of a particle moving along x - axis is given by U(x)=ax-bx^(2) . Find the equilibrium position of particle.

A particle of mass 4kg moves simple harmonically such that its PE (U) varies with position x, as shown. The period of oscillations is :-