What is the period of small oscillations of the block of mass $m$ if the springs are ideal and pulleys are massless?

If the maximum velocity and maximum acceleration of a particle executing $SHM$ are equal in magnitude,the time period will be .... $\sec$

$A$ particle of mass $m$ is executing oscillations about the origin on the $X-$axis. Its potential energy is $U(x) = k|x|^3$,where $k$ is a positive constant. If the amplitude of oscillation is $a$,then its time period $T$ is:

$A$ particle is performing a linear simple harmonic motion of amplitude $A$. When it is midway between its mean and extreme position,the magnitudes of its velocity and acceleration are equal. What is the periodic time of the motion?

$A$ particle of mass $5 \times 10^{-5} \ kg$ is placed at the lowest point of a smooth parabola $x^2 = 40y$ ($x$ and $y$ in $m$). If it is displaced slightly such that it is constrained to move along the parabola,the angular frequency of oscillation (in $rad/s$) will be approximately:

$A$ sphere of radius '$r$' is kept on a concave mirror of radius of curvature '$R$'. The arrangement is kept on a horizontal table. If the sphere is displaced from its equilibrium position and left,then it executes $S$.$H$.$M$. The period of oscillation will be ($g =$ acceleration due to gravity).