Class 11PhysicsOscillationsPeriodic, Oscillatory motion and its characteristics and types of SHM and Equation of SHM
MediumDefine simple harmonic motion and write its important characteristics.
(N/A) Simple Harmonic Motion $(SHM)$ is defined as the periodic motion of a body about a fixed point on a linear path,where the restoring force acting on the body is always directed towards the fixed point (mean position) and is directly proportional to the displacement of the body from that fixed point.
Mathematically,this is expressed as $F = -kx$,where $F$ is the restoring force,$x$ is the displacement from the mean position,and $k$ is the force constant.
Important characteristics of $SHM$:
$1$. The motion is periodic and oscillatory.
$2$. The restoring force is always directed towards the mean position.
$3$. The magnitude of the restoring force is directly proportional to the displacement from the mean position $(F \propto x)$.
$4$. The acceleration of the particle is also proportional to the displacement and directed towards the mean position $(a = -\omega^2 x)$.
$5$. $A$ body performing simple harmonic motion is called a Simple Harmonic Oscillator.
Mathematically,this is expressed as $F = -kx$,where $F$ is the restoring force,$x$ is the displacement from the mean position,and $k$ is the force constant.
Important characteristics of $SHM$:
$1$. The motion is periodic and oscillatory.
$2$. The restoring force is always directed towards the mean position.
$3$. The magnitude of the restoring force is directly proportional to the displacement from the mean position $(F \propto x)$.
$4$. The acceleration of the particle is also proportional to the displacement and directed towards the mean position $(a = -\omega^2 x)$.
$5$. $A$ body performing simple harmonic motion is called a Simple Harmonic Oscillator.
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Similar Questions
$A$ 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 SolutionWhich of the following functions of time represent $(a)$ simple harmonic,$(b)$ periodic but not simple harmonic,and $(c)$ non-periodic motion? Give period for each case of periodic motion ($\omega$ is any positive constant):
$(a)$ $\sin \omega t - \cos \omega t$
$(b)$ $\sin^3 \omega t$
$(c)$ $3 \cos (\pi/4 - 2 \omega t)$
$(d)$ $\cos \omega t + \cos 3 \omega t + \cos 5 \omega t$
$(e)$ $\exp(-\omega^2 t^2)$
$(f)$ $1 + \omega t + \omega^2 t^2$
$(a)$ $\sin \omega t - \cos \omega t$
$(b)$ $\sin^3 \omega t$
$(c)$ $3 \cos (\pi/4 - 2 \omega t)$
$(d)$ $\cos \omega t + \cos 3 \omega t + \cos 5 \omega t$
$(e)$ $\exp(-\omega^2 t^2)$
$(f)$ $1 + \omega t + \omega^2 t^2$
Medium
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
View SolutionThe motion of a particle as per $x = A \sin \omega t + B \cos \omega t$ is :-
Medium
View Solution$A$ particle is moving with constant angular velocity along the circumference of a circle. Which of the following statements is true?
Easy
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