Write the difference between oscillations and vibrations.

The displacement of a particle in an oscillatory motion at a time $t$ is given by $x = 8 \sin \frac{\pi t}{4} \text{ cm}$. Calculate its displacement in the time interval $t = 0 \text{ s}$ to $t = 2 \text{ s}$. (in $\text{ cm}$)

Which one of the following equations of motion represents simple harmonic motion? (Where $k, k_0, k_1$ and $a$ are all positive constants)

$A$ 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:

$A$ simple harmonic motion is represented by $\alpha \frac{d^2 x}{d t^2}+\beta x=0$. Its period is

The graphs in the figure show that a quantity $y$ varies with displacement $d$ in a system undergoing simple harmonic motion. Which graph best represents the relationship obtained when $y$ is the time?