Class 11

Oscillations question bank (Physics)

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Q1.

$A$ 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:

(A)
At points away from the origin,the particle is in unstable equilibrium
(B)
For any finite non-zero value of $x$,there is a force directed away from the origin
(C)
If its total mechanical energy is $k/2$,it has its minimum kinetic energy at the origin
(D)
For small displacements from $x = 0$,the motion is simple harmonic
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Q2.

$A$ particle of mass $m$ is under the influence of a force $F$ which varies with the displacement $x$ according to the relation $F = -kx + F_0$,where $k$ and $F_0$ are constants. The particle,when disturbed,will oscillate:

(A)
about $x = 0$ with $\omega \neq \sqrt{k/m}$
(B)
about $x = 0$ with $\omega = \sqrt{k/m}$
(C)
about $x = F_0/k$ with $\omega = \sqrt{k/m}$
(D)
about $x = F_0/k$ with $\omega \neq \sqrt{k/m}$
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