$A$ 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

The potential energy of a simple harmonic oscillator of mass $2 \,kg$ at its mean position is $5 \,J$. If its total energy is $9 \,J$ and amplitude is $1 \,cm$, then its time period is

The displacement of a particle,executing simple harmonic motion with time period $T$,is expressed as $x(t) = A \sin \omega t$,where $A$ is the amplitude. The maximum value of potential energy of this oscillator is found at $t = T / (2 \beta)$. The value of $\beta$ is . . . . . . .

For any $S.H.M.$,the amplitude is $6\, cm$. If the instantaneous potential energy is half the total energy,then the distance of the particle from its mean position is .... $cm$.

$A$ body is executing simple harmonic motion. At a displacement $x$,its potential energy is $E_1$ and at a displacement $y$,its potential energy is $E_2$. The potential energy $E$ at a displacement $(x+y)$ is

$A$ body executes simple harmonic motion. The potential energy $(P.E.)$,the kinetic energy $(K.E.)$ and total energy $(T.E.)$ are measured as a function of displacement $x$. Which of the following statements is true?