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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
The bob of a simple pendulum executes simple harmonic motion in water with a period $t$, while the period of oscillation of the bob is ${t_0}$ in air. Neglecting frictional force of water and given that the density of the bob is $(4/3) ×1000 kg/m^3$. What relationship between $t$ and ${t_0}$ is true
The displacement y of a particle executing periodic motion is given by $y = 4{\cos ^2}(t/2)\sin (1000t)$. This expression may be considered to be a result of the superposition of ........... independent harmonic motions
A weightless spring of length $60\, cm$ and force constant $200\, N/m$ is kept straight and unstretched on a smooth horizontal table and its ends are rigidly fixed. A mass of $0.25\, kg$ is attached at the middle of the spring and is slightly displaced along the length. The time period of the oscillation of the mass is
Two particles $P$ and $Q$ start from origin and execute Simple Harmonic Motion along $X-$axis with same amplitude but with periods $3$ seconds and $6$ seconds respectively. The ratio of the velocities of $ P$ and $Q$ when they meet is
A body executing simple harmonic motion has a maximum acceleration equal to $ 24\,metres/se{c^2} $ and maximum velocity equal to $ 16\;metres/sec $. The amplitude of the simple harmonic motion is
The potential energy of a simple harmonic oscillator at mean position is $2\,joules$. If its mean $K.E.$ is $4\,joules$, its total energy will be .... $J$
A particle of mass $200 \,gm$ executes $S.H.M.$ The restoring force is provided by a spring of force constant $80 \,N / m$. The time period of oscillations is .... $\sec$
A simple pendulum is suspended in a car. The car starts moving on a horizontal road according to equation $x\, = \,\frac{g}{2}\,\sqrt 3 {t^2}$. Find the time period of oscillation of the pendulum.
Two masses $m_1$ and $m_2$ are suspended together by a massless spring of constant $K$. When the masses are in equilibrium, $m_1$ is removed without disturbing the system. The amplitude of oscillations is