Consider 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

$A$ mass $m = 100 \, g$ is attached at the end of a light spring which oscillates on a frictionless horizontal table with an amplitude equal to $0.16 \, m$ and a time period equal to $2 \, s$. Initially,the mass is released from rest at $t = 0$ and displacement $x = -0.16 \, m$. The expression for the displacement of the mass at any time $t$ is:

Define simple harmonic motion and write its important characteristics.

For a particle performing $S.H.M.$,the equation is $\frac{d^2 x}{dt^2} + \alpha x = 0$. Then the time period of the motion will be

$A$ 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 a linear harmonic oscillator and a non-linear harmonic oscillator?