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) 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) 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 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 particle is moving with shm in a straight line. When the distance of the particle from the equilibrium position has the value x_1 and x_2 the corresponding values of velocities are v_1 and v_2 show that period is T=2pi[(x_2^2-x_1^2)/(v_1^2-v_2^2)]^(1//2)

A particle is moving with shm in a-straight line. When the distance of the particle from the equilibrium position has the values 2 cm and 4 cm, the corresponding values of velocities are 5 cms^(-1) and 3 cms^(-1) respectively. Find the length of the path and the period.

Define simple harmonic motion for a particle moving in a straight line.

A particle executing harmonic motion is having velocities v_1 and v_2 at distances is x_1 and x_2 from the equilibrium position. The amplitude of the motion is

A particle executing harmonic motion is having velocities v_1 and v_2 at distances is x_1 and x_2 from the equilibrium position. The amplitude of the motion is

A particle moves with a simple harmonic motion. If the velocities at distance of 4cm and 5cm from the equilibrium position are 13 cm per second and 5 cm per second respectively, find the period and amplitude. [Hint: Use the formula v= omegasqrt(a^(2)-x^(2)). ]