The total mechanical enegry of a particle is `E`. The speed of the particle at `x = ((2E)/(K))^(1//2)` is `((2E)/(m))^(1//2)`. Find the potential energy of the particle at `x` :

The total mechanical energy of a particle of mass m executing SHM with the help of a spring is E = (1//2)momega^(2)A^(2) . If the particle is replaced by another particle of mass m//2 while the amplitude A remains same. New mechanical energy will be :

The potential energy of a 1 kg particle free to move along the x- axis is given by V(x) = ((x^(4))/(4) - x^(2)/(2)) J The total mechainical energy of the particle is 2 J . Then , the maximum speed (in m//s) is

Force acting on a particle is F=-8x in S.H.M. The amplitude of oscillation is 2 (in m) and mass of the particle is 0.5 kg. The total mechanical energy of the particle is 20 J. Find the potential energy of the particle in mean position (in J).

The potential energy of a 2 kg particle free to move along the x- axis is given by V(x)[(x^(4))/(4)-(x^(2))/(2)]jou l e The total mechanical energy of the particle is 0.75 J . The maximum speed of the particle ( in m//s) is :

Potential energy of a particle in SHM along x - axis is gives by U = 10 + (x - 2)^(2) Here, U is in joule and x in metre. Total mechanical energy of the particle is 26 J . Mass of the particle is 2kg . Find (a) angular frequency of SHM, (b) potential energy and kinetic energy at mean position and extreme position, (c ) amplitude of oscillation, (d) x - coordinates between which particle oscillates.

The potential energy of a 1kg particle free to move along the x-axis is given by V(x)=(x^(4)/4-x^(2)/2)J The total mechanical energy of the particle is 2J then the maximum speed (in m//s) is

The potential energy of a particle of mass 1 kg free to move along x-axis is given by U(x) =(x^(2)/2-x) joule. If total mechanical energy of the particle is 2J then find the maximum speed of the particle. (Assuming only conservative force acts on particle)

The potential energy of a particle of mass m is given by U = (1)/(2) kx^(2) for x lt 0 and U=0 for x ge 0 . If total mechanical energy of the particle is E . Then its speed at x = sqrt((2E)/(k)) is

The potential energy of a particle of mass m is given by U=(1)/(2)kx^(2) for x lt 0 and U = 0 for x ge 0 . If total mechanical energy of the particle is E. Then its speed at x = sqrt((2E)/(k)) is