Class 11PhysicsOscillationsPeriodic, Oscillatory motion and its characteristics and types of SHM and Equation of SHM
MediumDefine simple harmonic motion $(SHM)$.
(N/A) Simple harmonic motion $(SHM)$ is a special type of periodic motion where the restoring force acting on a particle is directly proportional to its displacement from the mean position and is always directed towards the mean position.
Mathematically,it is expressed as $F = -kx$,where $F$ is the restoring force,$x$ is the displacement from the equilibrium position,and $k$ is the force constant.
In $SHM$,the acceleration of the particle is also proportional to its displacement and is given by $a = -\omega^2 x$,where $\omega$ is the angular frequency.
Mathematically,it is expressed as $F = -kx$,where $F$ is the restoring force,$x$ is the displacement from the equilibrium position,and $k$ is the force constant.
In $SHM$,the acceleration of the particle is also proportional to its displacement and is given by $a = -\omega^2 x$,where $\omega$ is the angular frequency.
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Similar Questions
What provides the restoring force in the following cases?
$(1)$ Compressed spring.
$(2)$ Displacement of water in a $U$-tube.
$(3)$ Displacement of a pendulum bob from its mean position.
$(1)$ Compressed spring.
$(2)$ Displacement of water in a $U$-tube.
$(3)$ Displacement of a pendulum bob from its mean position.
Easy
View Solution$A$ particle executing $SHM$ of amplitude $a$ has a displacement of $-\frac{a}{2}$ at $t = \frac{T}{4}$ and a positive velocity. Find the initial phase of the particle.
What is displacement? Explain its general meaning by giving examples.
Medium
View SolutionThe equation of motion of a particle is given by $x = a \sin(50t + \frac{\pi}{3}) \text{ cm}$. The particle will come to rest at time $t_1$ and it will have zero acceleration at time $t_2$. The $t_1$ and $t_2$ respectively are . . . . . . .
DifficultJEE MAIN 2026
View SolutionThe displacement of a particle varies with time according to the relation $x = a \sin \omega t + b \cos \omega t$.
Medium
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