Class 11PhysicsOscillationsPeriodic, Oscillatory motion and its characteristics and types of SHM and Equation of SHM
Difficult$A$ particle free to move along the $x$-axis has potential energy given by $U(x) = k[1 - \exp(-x^2)]$ for $-\infty \le x \le +\infty$,where $k$ is a positive constant of appropriate dimensions. Then:
- AAt points away from the origin,the particle is in unstable equilibrium
- BFor any finite non-zero value of $x$,there is a force directed away from the origin
- CIf its total mechanical energy is $k/2$,it has its minimum kinetic energy at the origin
- DFor small displacements from $x = 0$,the motion is simple harmonic
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Similar Questions
Which of the following functions of time represent $(a)$ periodic and $(b)$ non-periodic motion? Give the period for each case of periodic motion $[\omega$ is any positive constant].
$(i)$ $\sin \omega t + \cos \omega t$
$(ii)$ $\sin \omega t + \cos 2\omega t + \sin 4\omega t$
$(iii)$ $e^{-\omega t}$
$(iv)$ $\log(\omega t)$
$(i)$ $\sin \omega t + \cos \omega t$
$(ii)$ $\sin \omega t + \cos 2\omega t + \sin 4\omega t$
$(iii)$ $e^{-\omega t}$
$(iv)$ $\log(\omega t)$
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View SolutionDefine the amplitude of $SHM$ and draw two different $SHM$s in one figure having two different amplitudes.
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View SolutionThe displacement of a particle varies with time according to the relation $x = a \sin \omega t + b \cos \omega t$.
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View SolutionThe function $\sin^2(\omega t)$ represents:
MediumAIEEE 2005
View SolutionThe mass of a particle is $1\,kg$ and it is moving along the $x-$axis. The period of its small oscillation is $\frac{\pi}{2}$. Its potential energy may be:
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