The displacements of a particle executing SHM at three consecutive seconds are 6 cm, 10 cm and 6 cm respectively. Find out the frequency of oscillation of the particle.

The displacements of a particle executing SHM at three consecutive sec

1.	The displacements of a particle executing SHM at three consecutive seconds are 6 cm, 10 cm and 6 cm respectively. Find out the frequency of oscillation of the particle.
Answer» SOLUTION :DISPLACEMENT, `x=Acos(omegat+THETA)` LET initially at t = 0, displacement = 6 cm. So, at t = 1 s, displacement = 10 cm and at t = 2 s, displacement is = 6 cm `therefore" "6=Acostheta""...(1)` `10=Acos(omega+theta)""...(2)` `6=Acos(2omega+theta)""...(3)` From (1) and (3) we get, `cos(2omega+theta)=costheta=cos(-theta)` or, `2omega+theta=-thetaor,omega=-theta` `therefore" "` From (2), we get `10=Acos0or,A=10cm.` From (1), we get `6=10cos(-omega)or,cosomega=3/5` or, `omega=0.927"rad"*s^(-1)` `therefore"Frequency"=omega/(2pi)=0.927/(2xx3.14)=0.148s^(-1)`.