A particle is acted simultaneously by mutually perpendicular simple harmonic motion $$x=a \cos \omega t$$ and $$y=a \sin \omega t$$. The trajectory of motion of the particle will be

The displacement of a particle varies with time according to the relation $y=a \sin \omega t+b \cos \omega t$.

Four pendulums A, B, C and D are suspended from the same

elastic support as shown in figure. $A$ and $C$ are of the same length, while $B$ is smaller than $A$ and $D$ is larger than $A$. If $A$ is given a transerse displacement,

Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the $x$-projection of the radius vector of the rotating particle $P$ is

The equation of motion of a particle is $x=a \cos (\alpha t)^2$. The motion is