Embibe Experts Solutions for Exercise 3: Assignment

The time period of oscillation of a particle whose position varies with time $t$ as $x=(\sin \omega t+\sin 2\omega t+\sin 4\omega t)$ is

Which one of the following pairing is incorrect?

A particle $P$ is moving on a circular path of radius $R$ as shown in figure. If time period is $2$ minutes, then the equation of projection on $y$ axis for particle $P$ is (where $t$ is in seconds)

The shortest distance travelled by a particle executing $\mathrm{SHM}$ from extreme position in $3$ seconds is equal to half of its amplitude. The time period of given particle is

A particle executes $\mathrm{SHM}$ about $x=0$ along $x-$axis. The equation for $\mathrm{SHM}$ is $x=(10 \mathrm{cm})\sin \frac{\pi }{2}t,$ where $x$ is in $\mathrm{cm}$ and $t$ is in seconds. The maximum speed of particle is 

A block of mass $m$ is suspended from a massless spring of spring constant $\frac{2k}{3}$ as shown in figure. If block of mass $m$ is slightly displaced vertically downward and released, then it executes $\mathrm{SHM}.$ The time period of block is

Figure shows the velocity-time graph of an object executing $\mathrm{SHM}.$ The correct equation for displacement - time $(x-t)$ representing this motion is

A particle of mass $1 \mathrm{kg}$ is executing oscillation and its equation of motion is given by $2\frac{d^{2}x}{d{t}^2}+\frac{dx}{dt}+x=0.$ The motion is