Oscillations MCQs for NEET — Physics Questions with Answers

The text states: 'Simple harmonic motion is the simplest form of oscillatory motion. This motion arises when the force on the oscillating body is directly proportional to its displacement from the mean position, which is also the equilibrium position. Further, at any point in its oscillation, this force is directed towards the mean position.' Also, 'Only that periodic motion governed by the force law $ F = – k x $ is simple harmonic.'

The 'POINTS TO PONDER' section states: 'For linear simple harmonic motion with a given $ \omega $, two initial conditions are necessary and sufficient to determine the motion completely. The initial conditions may be (i) initial position and initial velocity or (ii) amplitude and phase or (iii) energy and phase.'

The 'POINTS TO PONDER' section clearly states: 'The period of SHM does not depend on amplitude or energy or the phase constant. Contrast this with the periods of planetary orbits under gravitation (Kepler’s third law).'

From the 'SUMMARY' section: 'The angular frequency $ \omega $ is related to the period and frequency of the motion by, $ \omega = 2\pi / T = 2\pi \nu $ (angular frequency).'

The NCERT text states: 'In practice, oscillating bodies eventually come to rest at their equilibrium positions because of the damping due to friction and other dissipative causes.' This describes damped oscillations.

Problem 13.1 from the exercises asks to identify periodic motions. An arrow released from a bow follows a parabolic trajectory but does not repeat its motion at regular intervals, making it non-periodic. The other options describe motions that repeat after a certain time.

The 'POINTS TO PONDER' section states: 'The motion of a simple pendulum is simple harmonic for small angular displacement.' For large angles, the motion is still periodic but not simple harmonic.

Point 6 from 'POINTS TO PONDER' states: 'A combination of two simple harmonic motions with arbitrary amplitudes and phases is not necessarily periodic. It is periodic only if frequency of one motion is an integral multiple of the other’s frequency. However, a periodic motion can always be expressed as a sum of infinite number of harmonic motions with appropriate amplitudes.' This decomposition of a general periodic function into a sum of harmonic functions is known as Fourier analysis, where the frequencies will typically be integer multiples of a fundamental frequency.

According to Newton's second law, F(t) = ma(t). For SHM, acceleration a(t) = -ω²x(t). Substituting this into Newton's second law gives F(t) = -mω²x(t). The text also defines k = mω², so F(t) = -kx(t). Therefore, all the given options are correct representations of the force law for SHM. (NCERT, page 267)

The context states: 'Like acceleration, force is always directed towards the mean position—hence it is sometimes called the restoring force in SHM.' This is a fundamental characteristic of SHM. (NCERT, page 267)