JEE Main202120 Jul 2021Evening ShiftPhysicsOscillationsActual
A particle is making simple harmonic motion along the X -axis. If at a distances x 1 and x 2 from the mean position the velocities of the particle are v 1 and v 2 , respectively. The time period of its oscillation is given as:
Options
- AT = 2 π x 2 2 + x 1 2 v 1 2 - v 2 2
- BT = 2 π x 2 2 + x 1 2 v 1 2 + v 2 2
- CT = 2 π x 2 2 - x 1 2 v 1 2 + v 2 2
- DT = 2 π x 2 2 - x 1 2 v 1 2 - v 2 2
Correct answer
D. T = 2 π x 2 2 - x 1 2 v 1 2 - v 2 2
Step-by-step solution
v 2 = ω 2   A 2 - x 2 A 2 = x 1 2 + v 1 2 ω 2 = x 2 2 + v 2 2 ω 2 ω 2 = v 2 2 - v 1 2 x 1 2 - x 2 2 T = 2 π x 1 2 - x 2 2 v 2 2 - v 1 2