Oscillations NEET PYQs (1995–2026)

Solved Oscillations PYQs

3 recent questions with answers. The full set of 66 is free to practise.

1. NEET 2026MediumSimple Harmonic Motion
   Q1

   A cylindrical cork of uniform density floats in a liquid of density ${\rho }_1$. If the cork is depressed slightly and released, it oscillates harmonically with time period $T$. If the same cork floats in another liquid of density ${\rho }_2$, then the similar oscillation has time period $2T$. The value of ${\rho }_2/{\rho }_1$ is:

   • A4
   • B2
   • C1/2
   • D1/4

   Show answer & solution

   Correct answer: (D)

   Time period of vertical oscillation of floating cylinder:
   
   $T=2\pi \sqrt{\frac{m}{\rho gA}}$ where $m$ is mass, $\rho$ is density
   
   of liquid, $A$ is cross-sectional area.
   
   $T\propto \frac{1}{\sqrt{\rho }}$.
   
   Given $T_2=2T_1$
   
   $\Rightarrow \frac{T_2}{T_1}=2=\sqrt{\frac{{\rho }_1}{{\rho }_2}}$.
   
   $$\frac{{\rho }_1}{{\rho }_2}=4$$
   
   $\Rightarrow \frac{{\rho }_2}{{\rho }_1}=\frac{1}{4}$.
2. NEET 2025MediumPendulums
   Q2

   Two identical point masses $P$ and $Q$, suspended from two separate massless springs of spring constants $k_1$ and $k_2$, respectively, oscillate vertically. If their maximum speeds are the same, the ratio ( $A_Q/A_P$ ) of the amplitude $AQ$ of mass $Q$ to the amplitude $A_P$ of mass $P$ is

   • A$\sqrt{\frac{k_2}{k_1}}$
   • B$\sqrt{\frac{k_1}{k_2}}$
   • C$\frac{k_2}{k_1}$
   • D$\frac{k_1}{k_2}$

   Show answer & solution

   Correct answer: (B)

   Given that the maximum velocities of $P$ and $Q$ are the same:
   
   $$v_P=v_Q$$
   
   This implies:
   
   $$A_P{\omega }_P=A_Q{\omega }_Q$$
   
   From this, the ratio of the amplitudes can be expressed as:
   
   $$\frac{A_Q}{A_P}=\frac{{\omega }_P}{{\omega }_Q}$$
   
   The angular frequency $\omega$ of a mass-spring system is given by:
   
   $$\omega =\sqrt{\frac{k}{m}}$$
   
   Thus, for the two masses:
   
   $${\omega }_P=\sqrt{\frac{k_1}{m}}\text{ and }{\omega }_Q=\sqrt{\frac{k_2}{m}}$$
   
   Substituting these into the ratio equation, we get:
   
   $$\frac{A_Q}{A_P}=\frac{\sqrt{\frac{k_1}{m}}}{\sqrt{\frac{k_2}{m}}}=\sqrt{\frac{k_1}{k_2}}$$
   
   Hence, the ratio of the amplitude of mass $Q$ to the amplitude of mass $P$ is:
   
   $$\sqrt{\frac{k_1}{k_2}}$$
3. NEET 2024MediumEnergy in SHM
   Q3

   A particle executing simple harmonic motion with amplitude $A$ has the same potential and kinetic energies at the displacement
   [NEET 2024 Re ]

   • A$2\sqrt{A}$
   • BA/2
   • C$A/\sqrt{2}$
   • D$A\sqrt{2}$

   Show answer & solution

   Correct answer: (C)

   Potential energy $=\frac{1}{2}k{x}^2$
   Kinetic energy $=\frac{1}{2}k{A}^2-\frac{1}{2}k{x}^2$
   According to given condition
   $$\frac{1}{2}k{x}^2=\frac{1}{2}k{A}^2-\frac{1}{2}k{x}^{2}k2x^2=k{A}^2{x}^2=\frac{A^2}{2}x=\frac{A}{\sqrt{2}}$$

Topic-wise question count

Where NEET has asked from Oscillations, most frequent first.

• Simple Harmonic Motion (Equation, velocity, acceleration etc)37
• Pendulums13
• Energy in SHM11
• Damped and forced Oscillations3
• Simple Harmonic Motion2

Year-wise Oscillations questions in NEET

Number of questions from this chapter in each year's paper(s).