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speed of particle is `sqrt(2)m//s` at `x = +- sqrt(2)m` Kinetic energy of the particle is `1J` at `x = +- sqrt(2)m` At `t = pi//6` sec. particle is at `x = -1 m`Kinetic energy is `1.5 J` at `x = +- 1m`

Answer :

A::B::DSolution :

`KE_(max)=(1)/(2)mv_(max)^(2)=TE` <br> `rArr v_(max)=sqrt((2xx2)/(1))=2 m//s` <br> amplitude `A = (v_(max))/(omega) = 2 m` <br> `x = A sin omega t = 2 sin t` <br> `v =2 cos t = sqrt(4 - x^(2))` <br> (A) `v = sqrt(2) m//s rArr x = pm sqrt(2) m` <br> (B) `KE = (1)/(2) mv_(2) rArr 1 = (1)/(2) xx 1 xx v_(2)` <br> `rArr v = sqrt(2) m//s` <br> `:. x = pm sqrt(2) m` <br> (C) at `t = pi//6 s, x =2 sin pi//6 = 1m` <br> (D) `KE = (3)/(2) rArr 1.5 =(1)/(2) xx mv_(2)` <br> `rArr v = sqrt(3) rArr x = pm 1 m`.