Embibe Experts Solutions for Chapter: Oscillations, Exercise 2: Level 2

The time period of oscillation of a mass $m$ suspended from a spring is $2 \mathrm{s}$. If a mass of $(\mathrm{m}+5) \mathrm{kg}$ is suspended from the same spring its time period is $3 \mathrm{s}$. What is the value of mass $m$?

A thin uniform rod of length $3.00 \mathrm{m}$ executes simple harmonic oscillations like a physical pendulum with minimum time period. If the effective length of pendulum is $\sqrt{x} \mathrm{m}$. Find the value of $x$.

A particle starts S.H.M. from mean position. Its amplitude is $a$. At one instant, its velocity is half of the maximum velocity. Its displacement at this instant is

 A body of mass $36 \mathrm{g}$ moves with S.H.M. of amplitude $A=13 \mathrm{cm}$ and time period $T=12 \mathrm{s}.$ At time $t=0,$ the displacement $\mathrm{x}$ is $+13$. The shortest time of passage from $x=+6.5 \mathrm{cm}$  to $\mathrm{x}=-6.5 \mathrm{cm}$ is

The velocity of a particle executing a simple harmonic motion is$13 \mathrm{m} {\mathrm{s}}^{-1},$ when its distance from the equilibrium position $\left(Q\right)$ is $3\mathrm{m}$ and its velocity is$12 \mathrm{m} {\mathrm{s}}^{-1},$ when it is $5\mathrm{m}$ away from $Q$. The frequency of the simple harmonic motion is

A particle has simple harmonic motion. The equation of its motion is $x=5\sin \left(4t-\frac{\pi }{6}\right)$ where $x$ is its displacement. If the displacement of the particle is $3$ units, then its velocity is

Two simple harmonic motions of angular frequency $100$ and $1000 \mathrm{rad} {\mathrm{s}}^{-1}$ have the same displacement amplitude. The ratio of their maximum accelerations is

The variation of acceleration $a$ and displacement $x$ of the particle executing $\mathrm{S}.\mathrm{H}.\mathrm{M}.$ is indicated by which of the following curves?