Question

At distances y has velocities v 1 m and y2 2 m from equilibrium, an oscillating particle 1 m/s, respectively. 2 m/s and v2

The Question: what is the period?

Please explain in details how to calculate the period.

Answer 1

For Harmonic oscillation- y(t) = A sin (wt + phi) (i) A is amplitude of oscillation phi is phase difference w is angular frequency y (t) is displacement of the particle at time �t� (Distance of the particle from equilibrium position) \r\n velocity V = dy (t)/dt = Aw cos (wt + phi) V = Aw squareroot 1 - sin^2 (wt + phi) Because cos^2 theta = 1 - sin^2 theta V = Aw squareroot 1 - (y (t)/A)^2 from equation (1) sin (wt + phi) = y(t)/A V = w squareroot A^2 - y(t)^2 (2) at y_1 = 1m v_1 = 2 m/s 2 = w squareroot A^2 - (1)^2 = > 2 w squareroot A^2 - 1 (3) at y_2 = 2m v_2 = 1m/s 1 = w squareroot A^2 - (2)^2 = > 1 = w squareroot A^2 -4 (6) \r\n Velocity V = dy (t)/dt = Aw cos (wt + phi) V = Aw squareroot 1 - sin^2