Class 11PhysicsOscillationsPeriodic, Oscillatory motion and its characteristics and types of SHM and Equation of SHM
MediumDefine simple harmonic motion. Write important characteristics of simple harmonic motion.
(N/A) Simple Harmonic Motion $(SHM)$ is a special type of periodic motion where the restoring force is directly proportional to the displacement from the mean position and is always directed towards the mean position. Mathematically,$F = -kx$,where $k$ is the force constant and $x$ is the displacement.
Important characteristics of $SHM$ are:
$1$. The motion is periodic and oscillatory.
$2$. The restoring force is always proportional to the displacement $(F \propto -x)$.
$3$. The acceleration of the particle is proportional to the displacement and directed towards the mean position $(a = -\omega^2 x)$.
$4$. The total mechanical energy of the system remains conserved.
$5$. The motion can be represented by a sine or cosine function,such as $x(t) = A \sin(\omega t + \phi)$.
Important characteristics of $SHM$ are:
$1$. The motion is periodic and oscillatory.
$2$. The restoring force is always proportional to the displacement $(F \propto -x)$.
$3$. The acceleration of the particle is proportional to the displacement and directed towards the mean position $(a = -\omega^2 x)$.
$4$. The total mechanical energy of the system remains conserved.
$5$. The motion can be represented by a sine or cosine function,such as $x(t) = A \sin(\omega t + \phi)$.
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Similar Questions
Out of the following functions representing the motion of a particle,which represent $SHM$?
$(A)\; y = \sin \omega t - \cos \omega t$
$(B)\; y = \sin^3 \omega t$
$(C)\; y = 5 \cos \left( \frac{3\pi}{4} - 3\omega t \right)$
$(D)\; y = 1 + \omega t + \omega^2 t^2$
$(A)\; y = \sin \omega t - \cos \omega t$
$(B)\; y = \sin^3 \omega t$
$(C)\; y = 5 \cos \left( \frac{3\pi}{4} - 3\omega t \right)$
$(D)\; y = 1 + \omega t + \omega^2 t^2$
MediumAIPMT 2011
View SolutionDefine periodic motion and oscillatory motion.
Medium
View SolutionThe displacement of a particle performing linear $S.H.M.$ is given by $y = A \cos[\pi(t + \phi)]$. If at $t = 0$, the displacement is $y = 2 \text{ cm}$ and velocity is $2\pi \text{ cm/s}$, the value of amplitude $A$ in $\text{cm}$ is
DifficultMHT CET 2026
View SolutionThe displacement of a particle in $SHM$ is given by $x = 5 \sin(\pi t)$,where $x$ is in $cm$. What is the time taken by the particle to travel from the mean position to the position of maximum displacement (in $, s$)?
Easy
View SolutionFill in the blanks:
$1.$ In $SHM$,......... quantities are always positive.
$2.$ $A$ periodic motion that obeys the force law ......... is only a simple harmonic motion.
$3.$ $A$ $SHO$ with a periodic time of $2 \ s$ starts its oscillation from the lower end of its path of motion; its phase will be .......... at time $t = 2 \ s$.
$1.$ In $SHM$,......... quantities are always positive.
$2.$ $A$ periodic motion that obeys the force law ......... is only a simple harmonic motion.
$3.$ $A$ $SHO$ with a periodic time of $2 \ s$ starts its oscillation from the lower end of its path of motion; its phase will be .......... at time $t = 2 \ s$.
Medium
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