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The equation of motion of a particle of mass $1\,g$ is $\frac{{{d^2}x}}{{d{t^2}}} + {\pi ^2}x = 0$ where $x$ is displacement (in $m$ ) from mean position. The frequency of oscillation is .... $s$ (in $Hz$ )
A uniform thin ring of radius $R$ and mass $m$ suspended in a vertical plane from a point in its circumference. Its time period of oscillation is ........
A particle moves with simple harmonic motion in a straight line. In first $\tau \,s$, after starting from rest, it travels a distance $a$, and in next $\tau \,s$, it travels $2a$ in same direction then
The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $T$. If along with it another mass $M$ is also suspended , the period of oscillation will now be
A particle of mass $m$ moves in a one-dimensional potential energy $U(x) = -ax^2 + bx^4,$ where $'a'$ and $'b'$ are positive constants. The angular frequency of small oscillations about the minima of the potential energy is equal to