Two SHMs `s_(1) = a sin omega t` and `s_(2) = b sin omega t` are superimposed on a particle. The `s_(1)` and `s_(2)` are along the direction which makes `37^(@)` to each other

Options

A. the particle will perform `S.H.M`
B. the particle will not perform `S.H.M`
C. the particle will perform period motion but not S.H.M
D. the motion will not be oscillatory

Answer

A

Explanation

Resultant displacement will be the vector sum of two displacements:
`S = sqrt(S_(1)^(2) + S_(2)^(2)+ 2S_(1)S_(2) cos 37^(@))`
`sqrt(a^(2) sin^(2) omega t^(2) + b^(2) sin^(2) omega t^(2) + 2ab sin^(2) omega t xx (4)/(5))`
`S = sqrt(a^(2) + b^(2) + (8ab)/(5)) sin omega t`
Which shown that the particle `SHM`