Class 11PhysicsOscillationsPeriodic, Oscillatory motion and its characteristics and types of SHM and Equation of SHM
EasyWhat is a linear harmonic oscillator and a non-linear harmonic oscillator?
(N/A) linear harmonic oscillator is a system where the restoring force $F$ is directly proportional to the displacement $x$ from the equilibrium position,i.e.,$F = -kx$,where $k$ is the force constant. The motion of such an oscillator is simple harmonic motion $(SHM)$.
$A$ non-linear harmonic oscillator is a system where the restoring force $F$ is not proportional to the displacement $x$. In such cases,the force can be expressed as a non-linear function of displacement,such as $F = -kx - ax^3$ or other higher-order terms. Consequently,the motion of a non-linear oscillator is not simple harmonic motion.
$A$ non-linear harmonic oscillator is a system where the restoring force $F$ is not proportional to the displacement $x$. In such cases,the force can be expressed as a non-linear function of displacement,such as $F = -kx - ax^3$ or other higher-order terms. Consequently,the motion of a non-linear oscillator is not simple harmonic motion.
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Similar Questions
Given below are two statements. One is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A) :$ Knowing initial position $x_0$ and initial momentum $p_0$ is enough to determine the position and momentum at any time $t$ for a simple harmonic motion with a given angular frequency $\omega$.
Reason $(R) :$ The amplitude and phase can be expressed in terms of $x_0$ and $p_0$. In the light of the above statements,choose the correct answer from the options given below $:$
Assertion $(A) :$ Knowing initial position $x_0$ and initial momentum $p_0$ is enough to determine the position and momentum at any time $t$ for a simple harmonic motion with a given angular frequency $\omega$.
Reason $(R) :$ The amplitude and phase can be expressed in terms of $x_0$ and $p_0$. In the light of the above statements,choose the correct answer from the options given below $:$
DifficultJEE MAIN 2025
View SolutionIf the displacement of a particle executing simple harmonic motion is given by $x = 0.5 \cos (125.6 t)$,then the time period of oscillation of the particle is nearly. (Here $x$ is displacement in metre and $t$ is time in second) (in $s$)
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 SolutionDefine periodic time.
Medium
View Solution$A$ particle moves on the $x-$axis according to the equation $x = x_0 \sin^2 \omega t$. Is the motion simple harmonic?
Medium
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