Class 11PhysicsOscillationsPeriodic, Oscillatory motion and its characteristics and types of SHM and Equation of SHM
DifficultDefine displacement variable and periodic function.
(N/A) $1$. Displacement Variable: In the context of oscillatory motion,the displacement variable represents the change in position of an object from its mean (equilibrium) position at any given time $t$. It is typically denoted by $x(t)$ or $y(t)$.
$2$. Periodic Function: $A$ function is called periodic if it repeats its values at regular intervals of time. Mathematically,a function $f(t)$ is periodic if $f(t + T) = f(t)$ for all $t$,where $T$ is a positive constant known as the time period of the function.
$2$. Periodic Function: $A$ function is called periodic if it repeats its values at regular intervals of time. Mathematically,a function $f(t)$ is periodic if $f(t + T) = f(t)$ for all $t$,where $T$ is a positive constant known as the time period of the function.
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Similar Questions
$A$ particle performs $SHM$ on the $x-$axis with a time period of $0.5 \, s,$ such that its velocity is zero at $x = -3 \, cm$ and at $x = 9 \, cm$. It was located at $x = 0$ and moving in the negative $x-$direction at $t = 0$. The equation of $SHM$ of the particle is:
Difficult
View SolutionWhat are the two basic characteristics of a simple harmonic motion?
Medium
View SolutionWhen a particle in linear $S.H.M.$ completes two oscillations,its phase increases by
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 SolutionConsider a one-dimensional potential $V(x)$ as shown in the figure below. $A$ classical particle of mass $m$ moves under its influence and has total energy $E$ as shown below. The motion is
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