2019-03-01_Physics_Times

sin sin( )

2

A A A t A t



    

sin sin( ) cos

2

t t t



    

4 4 8

T

t t

 





   

The particles can be represented on a circular path

on which they are in uniform circular motion.

The image of 1 formed by L 1 on x-axis represent

the equation x A t sinwhereas the image of 2

formed by L 2 on x-axis represent the equation

sin( )

2

x A t



 

The two images can meet each othere as the two

images travel in opposite direction to each other.

We reverse the motion of second particle.

The time of meeting is

/ 2

2 2 8

4

r

r

T

t

T

  

  

   



Where r- relative angular displacement

r-relative angular velocity..

The equations of the particles are

x A t x A t 1 sin & 2 sin( 2 )



   

When the particles meet each other

x x t t 1 2 sin sin( 2 )



    

( 1) ( )

2

  t n   n t 

Forn^0

2

t t



   (not possible)

For n 1

( )

2

t t



    

2

2 4 8

T

t t

 





   

With the help of this method we can find the other

times at which the particles meet each other, by

taking higher values of n

If t is (-)ve then the particles do not meet at that

time.

Time period (T) and amplitude (A) are same for two

particles which undergo SHM along the same line.

At one particular instant, one particle is at phase

Method-2 Method-

Note:

2.

Sol:

3

2



and other is at phase zero while moving in the

same direction. Find the time at which they will

cross each other.

Given that the equations of the two particles are

1

3

sin( )

2

x A t



 

x A t 2  sin( )