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 SHM
B. the path of particle is straight line
C. Both (a) and (b) are correct
D. Both (a) and (b) are wrong

Answer

C

Explanation

`X = S_(1) + S_(2)cos 37^(@)`
` = (a sin omega t + 0.8 b sin omega t)` ...(i)
`y = S_(2)sin 37^(@)`
`= 0.6 b sin omega t`
`sin omega t = (y)/(0.6 b)`
Substituting this value in Eq. (i), we have
`x = ((a + 0.8 b)/(0.6 b)) y`
this is equation of a straight line passing through origin.
.