The total energy of a simple harmonic oscillator is proportional to

An object of mass $0.2 \,kg$ executes simple harmonic motion along the $x$-axis with a frequency of $(\frac{25}{\pi}) \,Hz$. At the position $x=0.04 \,m$, the object has a kinetic energy of $0.5 \,J$ and a potential energy of $0.4 \,J$. The amplitude of oscillation is ............ $cm$.

What is the ratio of the kinetic energy at the mean position to the potential energy at $y = A / 2$ for a particle performing $SHM$ (in $: 1$)?

For a particle executing $S.H.M.$,the displacement $x$ is given by $x = A \cos \omega t$. Identify the graphs which represent the variation of potential energy $(P.E.)$ as a function of time $t$ and displacement $x$.

$A$ particle of mass $m$ is hanging vertically by an ideal spring of force constant $K$. If the mass is made to oscillate vertically,its total energy is

Explain and draw the graphs of kinetic energy, potential energy, and mechanical energy as a function of time for a particle in Simple Harmonic Motion $(SHM)$.