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#	Question	Answer
1	What is oscillatory motion?	A motion in which a body moves to and fro about a mean position.
2	What is the relation between frequency and period?	\( v = \frac{1}{T} \).
3	What is the general equation for the displacement in simple harmonic motion?	\( x(t) = A \cos(\omega t + \phi) \).
4	Does the function \( \sin \omega t + \cos \omega t \) represent SHM?	Yes. It can be written as \( \sqrt{2} \sin(\omega t + \pi/4) \).
5	What is the velocity of a particle in SHM?	\( v(t) = -\omega A \sin(\omega t + \phi) \).
6	What is the relation between angular frequency and force constant in SHM?	\( \omega = \sqrt{\frac{k}{m}} \).
7	What is the kinetic energy of a particle in SHM?	\( K = \frac{1}{2} m \omega^2 A^2 \sin^2(\omega t + \phi) \).
8	Where is the kinetic energy maximum in SHM?	At the mean position.
9	What is the time period of a simple pendulum for small oscillations?	\( T = 2\pi \sqrt{\frac{L}{g}} \).
10	What is the acceleration equation in SHM?	\( a(t) = -\omega^2 x(t) \).
11	Which of the following represents simple harmonic motion: \( a = -10x \) or \( a = -200x^2 \)?	\( a = -10x \).
12	Does the function \( \sin \omega t - \cos \omega t \) represent SHM?	Yes.
13	The piston in a locomotive has a stroke of 1.0 m and angular frequency of 200 rad/min. What is its maximum speed?	1.67 m s⁻¹.
14	What is the stroke of a piston in SHM if its amplitude is 0.5 m?	1.0 m.
15	Is there a significant physical difference between 'oscillation' and 'vibration'?	No — informally, low-frequency periodic motion (like a tree branch swaying) is called oscillation, while high-frequency motion (like a vibrating guitar string) is called vibration.
16	If \(f(t)=A\sin\omega t + B\cos\omega t\), how can this be rewritten as a single sine function \(D\sin(\omega t+\phi)\)?	\(D=\sqrt{A^2+B^2}\) and \(\phi=\tan^{-1}(B/A)\), giving \(f(t)=D\sin(\omega t+\phi)\).
17	A particle P moves clockwise on a circle of radius B with period 30s, starting at 90° from the x-axis. What is the SHM equation for its x-projection?	\(x(t)=B\sin\left(\tfrac{\pi}{15}t\right)=B\cos\left(\tfrac{\pi}{15}t-\tfrac{\pi}{2}\right)\) — amplitude B, period 30s, initial phase \(-\pi/2\). (Example 13.4)
18	Up to what angle does \(\sin\theta\) remain nearly equal to \(\theta\) (in radians), justifying the small-angle approximation for a simple pendulum?	Up to about 20° (Table 13.1): e.g. at 20°, \(\theta=0.349\) rad and \(\sin\theta=0.342\) — very close.
19	Is a combination of two simple harmonic motions with arbitrary amplitudes and phases always periodic?	No — it is periodic only if the frequency of one motion is an integral multiple of the other's. However, any periodic motion can be expressed as a sum of infinitely many harmonic motions (Fourier's theorem).
20	A pendulum's length is halved (its bob's mass is also changed, but that's irrelevant). By what factor does its period change?	\(1/\sqrt2\approx0.71\) (period decreases), since \(T=2\pi\sqrt{L/g}\propto\sqrt{L}\) and does not depend on mass. (NEET 2024)
21	A spring stretches 5 cm under a 10 N force. A 2 kg mass is attached and set oscillating. What is the period?	≈0.628 s, from \(k=F/x=200\) N/m and \(T=2\pi\sqrt{m/k}\). (NEET 2021)
22	An SHM particle has amplitude 3 cm. At x=2 cm from the mean position, its speed equals the magnitude of its acceleration (in consistent units). What is the period?	\(T=4\pi/\sqrt5\approx5.6\) s, from \(v=\omega\sqrt{A^2-x^2}=\omega\sqrt5\) and \(a=\omega^2x=2\omega^2\): setting \(\omega\sqrt5=2\omega^2\). (NEET 2017)
23	A simple pendulum of amplitude a (in displacement) and period T — what is its speed at displacement x=a/2?	\(v=\dfrac{\sqrt3\,\pi a}{T}\), from \(v=\omega\sqrt{a^2-(a/2)^2}=\omega a\sqrt3/2\) and \(\omega=2\pi/T\). (AIPMT 2010)
24	What is the phase difference between velocity and acceleration in SHM?	\(\pi/2\) — velocity leads displacement by \(\pi/2\), while acceleration is exactly out of phase with displacement (differs by \(\pi\)), so velocity and acceleration differ by \(\pi/2\). (AIPMT 2007)
25	Two pendulums of length 0.5 m and 2.0 m start swinging together. After how many oscillations of the shorter one will they next be in phase?	2, since \(T\propto\sqrt{L}\) gives \(T_{2.0}/T_{0.5}=2\) — the longer completes 1 oscillation while the shorter completes 2. (AIPMT 1999)
26	For a particle in SHM with \(x=A\cos(\omega t+\phi)\), what shape does a plot of momentum \(p=mv\) against displacement x trace out?	An ellipse, since \((p/m\omega A)^2+(x/A)^2=\sin^2(\omega t+\phi)+\cos^2(\omega t+\phi)=1\). (NEET/AIPMT 2013, Karnataka)