A particle is moving in SHM in a straight line. When the distance of the particle from equilibrium position has values `x_(1)` and `x_(2)` , the corresponding values of velocities are `u_(1)` and `u_(2)`. Show that time period of vibration is `T=2pi[(x_(2)^(2)-x_(1)^(2))/(u_(1)^(2)-u_(2)^(2))]^(1//2)`

(a) The motion of the particle in simple harmonic motion is given by x = a sin omega t . If its speed is u , when the displacement is x_(1) and speed is v , when the displacement is x_(2) , show that the amplitude of the motion is A = [(v^(2)x_(1)^(2) - u^(2)x_(2)^(2))/(v^(2) - u^(2))]^(1//2) (b) A particle is moving with simple harmonic motion is a straight line. When the distance of the particle from the equilibrium position has the values x_(1) and x_(2) the corresponding values of velocity are u_(1) and u_(2) , show that the period is T = 2pi[(x_(2)^(2) - x_(1)^(2))/(u_(1)^(2) - u_(2)^(2))]^(1//2)

A particle moves with simple harmonic motion in a straight line. When the distances of the particle from the equilibrium position are x_(1) and x_(2) , the corresponding velocities are u_(1) and u_(2) . Find the period of the moton.

A particle is executing SHM along a straight line. Its velocities at distances x_(1) and x_(2) from the mean position are v_(1) and v_(2) , respectively. Its time period is

A particle is executing SHM if u_(1) and u_(2) are the speeds of the particle at distances x_(1) and x_(2) from the equilibrium position, shown that the frequency of oscillation f=(1)/(2pi)((u_(1)^(2)-u_(2)^(2))/(x_(2)^(2)-x_(1)^(2)))

A particle is executing S.H.M. If u_(1) and u_(2) are the velocitiesof the particle at distances x_(1) and x_(2) from the mean position respectively, then

A particle vibrates in SHM along a straight line.Its greatest acceleration is 5 pi^(2)cms^(-2) and when its distance from the equilibrium position is 4cm ,the velocity of the particle is 3 pi cms^(-1)

The velocity of a particle in S.H.M. at positions x_(1) and x_2 are v_(1) and v_(2) respectively. Determine value of time period and amplitude.

If u_(1) and u_(2) are the selected in two system of measurement and n_(1) and n_(2) their nomerical values, then

If u_(1) and u_(2) are the units selected in two systems of measurement and n_(1) and n_(2) their numerical values, then