Out of the following functions representing motion of a particle which represents SHM? 1. x=sin^(3)omegat 2. x=1+omegat+omega^(2)t^(2) 3. x=cosomegat+cos3omegat+cos5omegat 4. x=sinomegat+cosomegat

Out of the following functions representing motion of a particle which

1.	Out of the following functions representing motion of a particle which represents SHM? 1. x=sin^(3)omegat 2. x=1+omegat+omega^(2)t^(2) 3. x=cosomegat+cos3omegat+cos5omegat 4. x=sinomegat+cosomegat
Answer» Only 1 Only 1 and 3 Only 1 and 4 Only 4 Solution :(1) `x=sin^(3)omegat=(1)/(4)(3sinomegat-sin3omegat)""(becausesin3theta=3sintheta-4sin^(3)THETA)` It REPRESENTS a periodic motion with time PERIOD, `T=(2pi)/(OMEGA)` but not SHM. (2). `x=1+omegat+omega^(2)t^(2)` It represents a non-periodic motion. (3) `x=cosomegat+cos3omegat+cos5omegat` It represents a periodic motion with time period `T=(2pi)/(omega)` but not SHM. (4) `x=sinomegat+cosomegat=sqrt(2)[(1)/(sqrt(2))sinomegat+(1)/(sqrt(2))cosomegat]` `=sqrt(2)[sinomegat"cos"(pi)/(4)+"sin"(pi)/(4)cosomegat]` `=sqrt(2)sin(omegat+(pi)/(4))` It represents a SHM with time period `T=(2pi)/(omega)`