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There is a simple pendulum hanging from the ceiling of a lift. When the lift is stand still, the time period of the pendulum is $T$. If the resultant acceleration becomes $g/4,$ then the new time period of the pendulum is
A point particle is acted upon by a restoring force $-k x^{3}$. The time-period of oscillation is $T$, when the amplitude is $A$. The time-period for an amplitude $2 A$ will be
An object of mass $0.2\, kg$ executes simple harmonic along $X-$ axis with frequency of $\frac{{25}}{\pi }Hz$. At the position $x = 0.04m$, the object has kinetic energy of $0.5 \,J$ and potential energy of $0.4\, J$ amplitude of oscillation in meter is equal to
A uniform spring of force constant $k$ is cut into two pieces, the lengths of which are in the ratio $1 : 2$. The ratio of the force constants of the shorter and the longer pieces is
A simple pendulum of length $L$ is constructed from a point object of mass $m$ suspended by a massless string attached to a fixed pivot point. $A$ small peg is placed a distance $2L/3$ directly below the fixed pivot point so that the pendulum would swing as shown in the figure below. The mass is displaced $5$ degrees from the vertical and released. How long does it take to return to its starting position?
A ring is hung on a nail. It can oscillate, without slipping or sliding $(i)$ in its plane with a time period $T_{1}$ and, $(ii)$ back and forth in a direction perpendicular to its plane, with a period $T _{2}$. the ratio $\frac{ T _{1}}{ T _{2}}$ will be
A pendulum suspended from the ceiling of a train has a period $T$, when the train is at rest. When the train is accelerating with a uniform acceleration a, the period of oscillation will