The x-coordinate of a particle moving on x-axis is given by `x = 3 sin 100 t + 8 cos^(2) 50 t`, where x is in cm and t is time in seconds. Which of the following is/are correct about this motion

Options

A. the motion of the particle is not S.H.M.
B. the amplitude of the S.H.M. of the particle is `5` units
C. the amplitude of the resultant S.H.M. is `sqrt(73)`
D. the maximum displacement of the particle from the origin is `9` units.

Answer

B, D

Explanation

`x = 3 sin 100t + 8cos^(2)50t`
`= 3 sin(100t) + 4(1+cos100t)`
`= 4 + 5sin(100t + 37^(@))`
Amplitude `= 5`
Maximum displacement
`= 4 + 5 = 9 cm`