The displacement of two identical particles executing `SHM` are represented by equations `x_(1) = 4 sin (10t+(pi)/(6)) & x_(2) = 5 cos (omegat)` For what value of `•`, energy of both the particles is same.

Options

A. 16 unit
B. 6 unit
C. 4 unit
D. 8 unit

Answer

D

Explanation

(d)The equation of displacement,
`x_(1)=4"sin"(10t+(pi)/(6))`
The energy of this equation,
`E_(1)=(1)/(2)momega_(1)^(2)a_(1)^(2)=(1)/(2)mxx10xx10 xx 4 xx 4`
The second equation of displacement
`x_(2)=5"cos"(omegat)`
The energy of this equation
`E_(2)=(1)/(2)momega_(2)^(2)a_(2)^(2)=(1)/(2)momega_(2)^(2)xx5xx5`
According to question
`because E_(1)=E_(2)`
`therefore (1)/(2)momega_(2)^(2)xx5xx5=(1)/(2)mxx10xx10xx4xx4`
`omega_(2)^(2)=(10xx10xx4xx4)/(5xx5)`
or `omega_(2)=sqrt(2xx2xx4xx4)`
`=2xx4=8` unit