The displacement of two particle of same mass executing SHM are represented by the equations
`x_1=4 sin (10t+pi/6) and x_2=5 cos(omegat)`
The value of `omega` for which the energies of both the particle remain same is,

Options

A. 16 unit
B. 6 unit
C. 18 unit
D. 8 unit

Answer

d

Explanation

`x_1=4sin(10t-pi/6),omega_1=10,a=4`
Energy`E_1=1/2momega_1^2 a_1^2`,
`=1/2xxmxx(10)^2xx(4)^2`
`x_2=5cos(omegat)`
Energy,`E_2=1/2Momega_2^2 a_2^2`
`1/2xxmxxomega_2^2xx(5)^2`
Since,`E_1=E_2`
`implies1/2xxmxx(10)^2xx(4)^2=1/2xxmxxomega_2^2xx(5)^2`
`omega_2^2=((10)^2xx(4)^2)/(5)^2=64`
`omega_2=8`