A 20g particle is subjected to two simple harmonic motions `x_1=2sin10t`,`x_2=4sin(10t+(pi)/(3))`. Where `x_1` and `x_2` are in metres and t is in seconds.

Options

A. the displacement of the particle at `t=0` will be `2sqrt3` m
B. maximum speed of the particle will be `20sqrt7(m)/(s)`
C. Magnitude of maximum acceleration of the particle will be `200sqrt7(m)/(s^2)`
D. Energy of the result motion will be 28 J

Answer

A, B, C, D

Explanation

At `t=0`
Displacement,`x=x_1+x_2=4sin((pi)/(3))=2sqrt3`m
resulting amplitude `A=sqrt(2^2+4^2+2(2)(4)(cospi)/(3))`
`=2sqrt7`m
Maximum speed, `Aomega=20sqrt7(m)/(s)`
Maximum acceleration, `Aomega^2=200sqrt7(m)/(s^2)`
Energy of the motion `=(1)/(2)momega^2A^2=28J`