Embibe Experts Solutions for Chapter: Oscillations, Exercise 3: Level 3

A particle is executing SHIM in both$x$  and $y$ directions whose equations are as follows:$x=\cos \left(\pi t\right)$ and $y=\cos \left(\frac{\pi t}{2}\right)$. What will be the net trajectory of the particle on the $x-y$ plane?

The example of forced vibration is

Which of the following figure represents damped S.H.M.?

The amplitude of a damped oscillator becomes half in one minute. The amplitude after $3$ minute will be$\frac{1}{x}$ times the original, where $x$ is

Two simple harmonic motions are represented by $y_1=4 \sin \left(4\pi t+\frac{\pi }{2}\right)$ and $y_2=3 \cos \left(4\pi t\right).$ The resultant amplitude is :

A particle of mass $m$ moves along $x-$ axis under a force which is given by:

$F\left(x\right)=-Ax\left[1-e^{-k{x}^2}\right]$

Where $x$ is the position; while $A, k$ are constants. If the amplitude of oscillation be $a,$ and the time period be $T$ then

Study the following statements and find which is/are true.

$\mathrm{I}.$ The motion of the pendulum with the effect of dissipative force is known as damped oscillation.

$\mathrm{II}.$ Swinging of a child in a swing (without external push) is an example of free oscillation.

Choose correct option.

Motion of a particle can be described in $x$-direction by, $x=a \sin \omega t$ and $y$-direction by, $y=b \cos \omega t$. The particle is moving in,