Two particles are executing S.H.M. according to the equations `x_(1)=6sin(10pit+pi//3)andx_(2)=5cos(8pit+pi//4)` Then the phase difference between the

Question

Two particles are executing S.H.M. according to the equations `x_(1)=6sin(10pit+pi//3)andx_(2)=5cos(8pit+pi//4)` Then the phase difference between the

Two particles are executing S.H.M. according to the equations
`x_(1)=6sin(10pit+pi//3)andx_(2)=5cos(8pit+pi//4)`
Then the phase difference between the first and second particle at t = 0.5 s will be
A. `(7pi)/(12)`
B. `(13pi)/(12)`
C. `(25pi)/(12)`
D. `(pi)/(12)`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - A
`x_(1)=6sin(10pit+(pi)/(3))`
`x_(2)=5cos(8pit+(pi)/(4))`
`=5sin(8pit+(pi)/(2)=(pi)/(4))`
`deltaphi=phi_(1)-phi_(2)`
`=(10pit+(pi)/(3))-(8pit+(pi)/(2)+(pi)/(4))`
`=2pit+(pi)/(3)-((pi)/(2)+(pi)/(4))`
`=2pixx0.5+(pi)/(3)-[(2pi+pi)/(4)]`
`=(pi+(pi)/(3))-(3pi)/(4)=((3pi+pi)/(3))-((3pi)/(4))`
`=(4pi)/(3)(3pi)/(4)=(16pi-9pi)/(12)`
`=(17)/(12)pi`