Oscillations MCQs for NEET — Physics Questions with Answers

$y_1=\frac{A}{2}=A\sin \omega t$

$\Rightarrow \omega t=30°$

$y_2=\frac{A}{2}=A\sin \left(\omega t+\varphi \right)$

$\Rightarrow \omega t+\varphi =150°$

$\therefore$phase difference

       $\varphi =150°-30°$

         = $120=\frac{2\mathrm{\pi }}{3}rad$

The particle will come after a time $\frac{T}{4}$ to its mean position.

For the given super imposing waves

a₁ = 3, a₂ = 4 and phase difference $\varphi =\frac{\pi }{2}$

⇒ $A=\sqrt{a_1^2+a_2^2+2a_1{a}_2\cos \pi /2}=\sqrt{{\left(3\right)}^2+{\left(4\right)}^2}=5$

According to the NCERT text, 'Circular motion is a periodic motion, but it is not oscillatory.' Oscillatory motion specifically involves movement to and fro about a mean position. Orbital motion of a planet is periodic as it repeats after a fixed interval, but it does not oscillate about a mean position.

The NCERT text states, 'Here, the object moves to and fro about a mean position. The pendulum of a wall clock executes a similar motion. Examples of such periodic to and fro motion abound... Such a motion is termed as oscillatory motion.' While all oscillatory motions are periodic, not all periodic motions are oscillatory.

The 'POINTS TO PONDER' section states: 'The period T is the least time after which motion repeats itself. Thus, motion repeats itself after nT where n is an integer.' While T is the least time, the motion also repeats after any integral multiple of T.

The 'SUMMARY' section states: 'The period T is the time required for one complete oscillation, or cycle. It is related to the frequency $ \nu $ by, $ \nu = 1/T $.'

The 'SUMMARY' section specifies: 'The frequency $ \nu $ of periodic or oscillatory motion is the number of oscillations per unit time. In the SI, it is measured in hertz : 1 hertz = 1 Hz = 1 oscillation per second = $ 1s^{-1} $.'

The NCERT text mentions: 'There is no significant difference between oscillations and vibrations. It seems that when the frequency is small, we call it oscillation (like, the oscillation of a branch of a tree), while when the frequency is high, we call it vibration (like, the vibration of a string of a musical instrument).'

From the 'SUMMARY' section: 'In simple harmonic motion (SHM), the displacement x(t) of a particle from its equilibrium position is given by, $ x (t) = A \cos ( \omega t + \phi ) $ (displacement), in which A is the amplitude of the displacement, the quantity $ ( \omega t + \phi ) $ is the phase of the motion, and $ \phi $ is the phase constant.'