D. C. Pandey Solutions for Chapter: Simple Harmonic Motion, Exercise 2: Excercise 2

A cylindrical plastic bottle of negligible mass is filled with $310 \mathrm{mL}$ of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency $\omega$. If the radius of the bottle is $2.5 \mathrm{cm}$, then $\omega$ is close to (take density of water $={10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$),

A particle executes simple harmonic motion with an amplitude of $5 \mathrm{cm}$. When the particle is at $4 \mathrm{cm}$ from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time (in $\mathrm{seconds}$) is,

A simple harmonic motion is represented by $y=5(\sin 3\pi t+\sqrt{3}\cos 3\pi t) \mathrm{cm}$. The amplitude and time period of the motion are