What are the quantities that remain constant during the motion of the particle ? [(2+1+1)+1]

Name the quantity which remains unchanged during the flight of an oblique projectile.

What can be the cause of helical motion of charged particle ?

The kinetic energy of a particle is 1/2momega^(2)(A^(2)-x^(2)) , where m, omega and A are constants. Prove that the motion of the particle is simple harmonic.

Potential energy of a particle is 1/2momega^(2)x^(2) , where m and omega are constants. Prove that the motion of the particle is simple harmonic.

A particle moves along a straight line with a retardations of av^(n+1) , where v is the velocity at time t and a is a positive constant. If at t = 0 the velocity of the particle is u, show that at = (1)/(n)((1)/(v^(n))-(1)/(u^(n))).

What are the two constant quantities for Boyle's law?