$A$ particle executes simple harmonic motion according to the equation $4 \frac{d^2 x}{d t^2} + 320 x = 0$. Its time period of oscillation is .........

$A$ particle of mass $10\, g$ moves in a field where potential energy per unit mass is given by the expression $v = 8 \times 10^4\, x^2\, \text{erg/g}$. If the total energy of the particle is $8 \times 10^7\, \text{erg}$,then the relation between $x$ and time $t$ is:

Write the phase difference between displacement and velocity,displacement and acceleration,and velocity and acceleration for a particle executing Simple Harmonic Motion $(SHM)$.

Define periodic motion and oscillatory motion.

$A$ particle of mass $4 \text{ mg}$ is executing simple harmonic motion along the $x$-axis with an angular frequency of $40 \text{ rad s}^{-1}$. If the potential energy of the particle is $V(x) = a + bx^2$, where $V(x)$ is in joule and $x$ is in metre, then the value of $b$ 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: