Amplitude of a $SHO$ is $\sqrt{5} \ cm$. At what displacement from the mean position the ratio of kinetic energy to potential energy is $4$ (in $cm$)?

An object of mass $0.2 \ kg$ executes simple harmonic oscillations along the $X$-axis with a frequency of $(\frac{25}{\pi}) \ Hz$. At the position $x=0.04 \ m$,the object has kinetic energy $1 \ J$ and potential energy $0.6 \ J$. The amplitude of oscillation is (in $m$)

$A$ particle undergoing simple harmonic motion has an amplitude of $10 \ cm$. When the particle is at a displacement of $6 \ cm$ from the centre,then the ratio of its kinetic energy to potential energy is

The displacement of a particle executing $SHM$ is given by $y = 5 \sin \left(4t + \frac{\pi}{3}\right)$. If $T$ is the time period and the mass of the particle is $2 \text{ g}$, the kinetic energy of the particle when $t = \frac{T}{4}$ is given by (in $\text{ J}$)

Consider a simple harmonic motion $(SHM)$. Let $K$ and $U$ be kinetic energy and potential energy when the displacement in $SHM$ is one-half $\left(\frac{1}{2}\right)$ the amplitude. Which of the following statements is correct?

The potential energy of a simple harmonic oscillator,when the particle is halfway to its endpoint,is