$A$ body of mass $1 \ kg$ is executing simple harmonic motion $(SHM)$. Its displacement $y$ (in $cm$) at time $t$ is given by $y = 6 \sin (100 t + \pi/4) \ cm$. Its maximum kinetic energy is (in $J$)

The potential energy of a simple harmonic oscillator of mass $2\, kg$ in its mean position is $5\, J.$ If its total energy is $9\, J$ and its amplitude is $0.01\, m,$ its time period would be

The kinetic energy of a particle executing simple harmonic motion at a displacement of $3 \ cm$ from the mean position is $4 \ mJ$. If the amplitude of the particle is $5 \ cm$,then the maximum force acting on the particle is (in $N$)

The maximum restoring force of a body executing $SHM$ is $\alpha$ and the total energy is $\beta$. Obtain its amplitude in terms of $\beta$ and $\alpha$.

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 in meters is equal to:

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 $(SHM)$.