A particle executing simple harmonic motion with amplitude A has the same potential and kinetic energies at the displacement

The two-dimensional motion of a particle, described by $$\vec{r}=(\hat{i}+2 \hat{j}) A \cos \omega t$$ is a/an:

A. parabolic path

B. elliptical path

C. periodic motion

D. simple harmonic motion

Choose the correct answer from the options given below:

If $$x=5 \sin \left(\pi t+\frac{\pi}{3}\right) \mathrm{m}$$ represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are

If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is $$\frac{x}{2}$$ times its original time period. Then the value of $$x$$ is: