Two simple pendulum, first a bob of mass $M_1$ and length $L_1$ and second a bob of mass $M_2$ and length $L_2. M_1=M_2$ and $L_1=2L_2$. If the vibrational energy of both is same, then, which one is correct?

A man weighing  $60 \mathrm{kg}$ stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude $0.1 \mathrm{m}$ and frequency $\frac{2}{\pi } \mathrm{Hz}$. Which of the following statements is correct?

A particle of mass $m$ is moving in the $x-y$ plane such that its $x$ and $y$ coordinates vary according to the law, $x=a \sin \left(\omega t\right)$ and $y=a \cos \left(\omega t\right)$ where, $a$ and $\omega$ are positive constants and $t$ is time. Find equation of the path. Name the trajectory (path).