Class 11PhysicsOscillationsPeriodic, Oscillatory motion and its characteristics and types of SHM and Equation of SHM
MediumWhat is a linear harmonic oscillator? And what is a non-linear oscillator?
(N/A) linear harmonic oscillator is a system where the restoring force $F$ acting on a particle is directly proportional to its displacement $x$ from the equilibrium position,expressed as $F = -kx$,where $k$ is a constant.
In a non-linear oscillator,the restoring force is not strictly proportional to the displacement. It may contain higher-order terms of the displacement,such as $x^2, x^3, \dots$,meaning the force is expressed as $F = -kx - ax^2 - bx^3 - \dots$. These systems do not follow simple harmonic motion.
In a non-linear oscillator,the restoring force is not strictly proportional to the displacement. It may contain higher-order terms of the displacement,such as $x^2, x^3, \dots$,meaning the force is expressed as $F = -kx - ax^2 - bx^3 - \dots$. These systems do not follow simple harmonic motion.
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Similar Questions
Match the following functions with their corresponding nature of motion, where $\omega$ is a constant:
List-$I$
List-$II$
$A$. $\sin^2 \omega t$
$I$. Periodic but not $SHM$ $(T = 2\pi/\omega)$
$B$. $\sin^3 \omega t$
$II$. Periodic but not $SHM$ $(T = \pi/\omega)$
$C$. $\sin \omega t + \cos \pi \omega t$
$III$. Non-periodic
$D$. $\cos \omega t + \cos 2\omega t$
$IV$. Periodic but not $SHM$ $(T = 2\pi/\omega)$
| List-$I$ | List-$II$ |
| $A$. $\sin^2 \omega t$ | $I$. Periodic but not $SHM$ $(T = 2\pi/\omega)$ |
| $B$. $\sin^3 \omega t$ | $II$. Periodic but not $SHM$ $(T = \pi/\omega)$ |
| $C$. $\sin \omega t + \cos \pi \omega t$ | $III$. Non-periodic |
| $D$. $\cos \omega t + \cos 2\omega t$ | $IV$. Periodic but not $SHM$ $(T = 2\pi/\omega)$ |
DifficultJEE MAIN 2026
View Solution$A$ particle moves in the $x-y$ plane according to the equation $\overrightarrow{r} = (\widehat{i} + 2\widehat{j}) A \cos \omega t$. The motion of the particle is:
Difficult
View SolutionThe motion of a particle varies with time according to the relation $y = a(\sin \omega t + \cos \omega t)$.
Difficult
View SolutionThe motion of a particle as per $x = A \sin \omega t + B \cos \omega t$ is :-
Medium
View SolutionIf a $SHM$ is represented by $\frac{d^2x}{dt^2} + ax = 0$,its time period is:
Medium
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