Question

Two particles are executing shm in a straight line with same amplitude a and time period t. At time t=0, one particle is at displacement x1=+a and the other at x2=a/2 and they are approaching towards each other. After what time they cross each other?

Answer 1

Let the equation of each particle in SHM is given by, $x=asin\omega t$

displacement of first particle , x = +a
e.g., angular displacement = π/2

displacement of 2nd particle, x = -a/2 [ negative sign indicates that 2nd particle approach the first particle ]
e.g., angular displacement = π/6

so, angular separation or phase difference = π/2 - π/6 = π/3

now, t = $\frac{\theta}{\omega}$

we know, $\omega$ = 2π/T

so, t = π/3/(2π/T) = T/6

hence, after T/6 time they cross each other .

Answer 2

Let the equation of each particle in SHM is given by,  

displacement of first particle , x = +a

e.g., angular displacement = π/2

displacement of 2nd particle, x = -a/2 [ negative sign indicates that 2nd particle approach the first particle ]

e.g., angular displacement = π/6

so, angular separation or phase difference = π/2 - π/6 = π/3

now, t =  

we know,  = 2π/T

so, t = π/3/(2π/T) = T/6

hence, after T/6 time they cross each other .

thats it m8 pls mark as brainliest