$U$ is the potential energy $(PE)$ of an oscillating particle and $F$ is the force acting on it at a given instant. Which of the following is true?

What is the displacement of a body in $SHM$ when the potential energy becomes three times its kinetic energy?

$A$ block is in simple harmonic motion $(S.H.M)$ at the end of a spring with position given by $x = 5 \cos \left(\omega t + \frac{\pi}{4}\right)$. If the total mechanical energy is $100 \ J$, then the potential energy at time $t = 0$ is: (in $J$)

The kinetic energy,$K$ of a body performing simple harmonic motion varies with time $t$,is indicated in graph

$A$ particle starting from mean position executes simple harmonic motion with a period $8 \ s$. The minimum time in which its potential energy becomes half of the total energy is . . . . . . . (in $s$)

$A$ body is performing simple harmonic motion with an amplitude of $10 \, cm$. The velocity of the body is tripled by an air jet when it is at $5 \, cm$ from its mean position. The new amplitude of vibration is $\sqrt{x} \, cm$. The value of $x$ is . . . . . . .