Question

Two particles P and Q describe simple harmonic motions with same period, same amplitude along the same line and about the same equilibrium position O. When P and Q are on opposite sides of O at the same distance from O they have the same speed of 1.2m/s in the same direction. Again when their displacement are the same, they have the same speed of 1.6m/s in opposite directions. The maximum velocity in m/s of either particle is

Answer 1

Given :

The velocities of P and Q when they are  at same distance from O = 1.2 m/s

The velocities of P and Q when their displacements are same = 1.6 m/s

To find :

The maximum velocity of either of the particles = ?

Solution :

• Both the particles have same velocity when they are  at same distance from O

       AωCos∅ = 1.2…… (1)

• Both the particles have same velocity when they have same displacements

        AωSin∅ = 1.6………(2)

• By solving equations (1) and (2)

      Tan∅ = 4/3

       ∅ = 53°

• Substituting the value in equation (1)

       Aω (3/5) = 1.2

       Aω = 2m/s

The maximum velocity of particles is 2 m/s