- #1
vissh
- 82
- 0
elllllo :D
<Q>A particle is subjected to 2 simple harmonic motions in the same direction having equal amplitudes and equal frequency. If the resultant amplitude is equal to the individual motions,find the phase difference between the individual motions.
>Let x1 = A1sin(wt) and x2 = A2sin(wt + a)
Then, the resultant motion is also a SHM given by : x = A sin(wt +b)
where A = [(A1)2 +(A2)2 + 2(A2)(A1) cos(a) ] 1/2
Let the amplitude of individual motions was "A" and the phase difference was "d".
So, A = [ A2 + A2 + 2(A)(A)cosd ] 1/2
=> A= A [ 2 + 2cosd]1/2
=> 2 + 2cosd = 1
=> cosd = -(1/2)
=> d = 2[tex]\pi[/tex]/3 or 4[tex]\pi[/tex]/3 [taking values b/w [0,2[tex]\pi[/tex]]
But the answer got only 2[tex]\pi[/tex]/3
Did i did wrong at some place ?
Thanks for reading (^.^)
Homework Statement
<q><Q>A particle is subjected to 2 simple harmonic motions in the same direction having equal amplitudes and equal frequency. If the resultant amplitude is equal to the individual motions,find the phase difference between the individual motions.
Homework Equations
>Let x1 = A1sin(wt) and x2 = A2sin(wt + a)
Then, the resultant motion is also a SHM given by : x = A sin(wt +b)
where A = [(A1)2 +(A2)2 + 2(A2)(A1) cos(a) ] 1/2
The Attempt at a Solution
Let the amplitude of individual motions was "A" and the phase difference was "d".
So, A = [ A2 + A2 + 2(A)(A)cosd ] 1/2
=> A= A [ 2 + 2cosd]1/2
=> 2 + 2cosd = 1
=> cosd = -(1/2)
=> d = 2[tex]\pi[/tex]/3 or 4[tex]\pi[/tex]/3 [taking values b/w [0,2[tex]\pi[/tex]]
But the answer got only 2[tex]\pi[/tex]/3
Did i did wrong at some place ?
Thanks for reading (^.^)