The displacement of a particle represented by the equation y= 3 cos((pi)/(4)-2 omega t). The motion of the particle is

The displacement of a particle represented by the equation y= 3 cos((p

1.	The displacement of a particle represented by the equation y= 3 cos((pi)/(4)-2 omega t). The motion of the particle is
Answer» SIMPLE harmonic with period `(2pi)/(omega)` simple harmonic with period `(pi)/(omega)` periodic but not simple harmonic non-periodic Solution :The displacement of motion of particle `y= 3 cos ((pi)/(4)- 2omega t)` `therefore v= (d)/(DT)[3 cos ((pi)/(4)- 2omega t)]` `= 3(-2omega) [-sin((pi)/(4)- 2omega t)]` `therefore v = 6 omega sin ((pi)/(4)-2omega t)` Acceleration, `a= (dv)/(dt)= (d)/(dt) [6OMEGA sin ((pi)/(4)-2omega t)]` `therefore a = 6omega xx (-2omega)cos((pi)/(4)- 2omega t)` `= -12omega^(2) cos ((pi)/(4)- 2omega t)` `= -4omega^(2) [3cos ((pi)/(4)- 2omega t)]` `therefore a= -4omega^(2)y"""........"(1)` `therefore a propto -y` This is CONDITION of simple harmonic motion, the motion is SHM and `omega.= 2 omega""[therefore " Comparing equation (1) with "a= -(omega.)^(2)y]` `therefore (2pi)/(T.)= 2omega` `therefore T.= (2pi)/(2omega)= (pi)/(omega)`