A `20gm` particle is subjected to two simple harmonic motions
`x_(1)=2 sin 10t,`
`x_(2)=4 sin (10t+(pi)/(3))`, where `x_(1) & x_(2)` are in metre `& t ` is in `sec`.

Options

A. The displacement of the particle at t=0 will be `2sqrt(3)m`
B. Maximum speed of the particle will be `20sqrt(7) m//s`.
C. Magnitude of maximum acceleration of the particle will be `200sqrt(7) m//s^(2)`
D. Energy of the resultant simple harmonic motion will be 28 J

Explanation

At t= 0
Displacement `x=x_(1)+x_(2)=4 sin ((pi)/3) =2sqrt(3) m`.
Resulting Amplitude `A=sqrt(2^(2)+4^(2)+2(2)(4) cos pi//3)=sqrt(4+16+8)=sqrt(28) =2sqrt(7) m`
Maximum speed `=A omega=20 sqrt(7) m//s`
Maximum acceleration `Aomega^(2)=200sqrt(7) m//s^(2)`
Energy of the motion =`1/2 m omega^(3)A^(2) =28 J Ans.`