JEE Main Physics — Waves & Oscillations previous year questions with solutions.
A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency $\omega$. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time
Starting from the origin, a body oscillates simple harmonically with a period of $2 \mathrm{~s}$. After what time will its kinetic energy be $75 \%$ of the total energy?
A string is stretched between fixed points separated by $75 \mathrm{~cm}$. It is observed to have resonant frequencies of $420 \mathrm{~Hz}$ and $315 \mathrm{~Hz}$. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is
When two tuning forks (fork 1 and fork 2) are sounded simultaneously, 4 beats per second are heard. Now, some tape is attached on the prong of the fork 2 . When the tuning forks are sounded again, 6 beats per seconds are heard. If the frequency of fork 1 is $200 \mathrm{~Hz}$, then what was the original frequency of fork 2 ?
Two simple harmonic motions are represented by the equation $\mathrm{y}_1=0.1$ $\sin \left(100 \pi t+\frac{\pi}{3}\right)$ and $y_2=0.1 \cos \pi t$. The phase difference of the velocity of particle 1 w.r.t. the velocity of the particle 2 is
If a simple harmonic motion is represented by $\frac{\mathrm{d}^2 \mathrm{x}}{\mathrm{dt}^2}+\alpha \mathrm{x}=0$, its time period is
The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillation bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would
The function $\sin ^2(\omega t)$ represents
A particle at the end of a spring executes simple harmonic motion with a period $t_1$, while the corresponding period for another spring is $t_2$. If the period of oscillation with the two springs in series is $\mathrm{t}$, then
The total energy of particle, executing simple harmonic motion is
A particle of mass $m$ is attached to a spring (of spring constant $k$ ) and has a natural angular frequency $\omega_0$. An external force $F(t)$ proportional to $\cos \omega t\left(\omega \neq \omega_0\right)$ is applied to the oscillator. The time displacement of the oscillator will be proportional to
In forced oscillation of a particle the amplitude is maximum for a frequency $\omega_1$ of the force, while the energy is maximum for a frequency $\omega_2$ of the force, then
The bob of a simple pendulum executes simple harmonic motion in water with a period $t$, while the period of oscillation of the bob is $t_0$ in air. Neglecting frictional force of water and given that the density of the bob is $\left(\frac{4}{3}\right) \times 1000 \mathrm{~kg} / \mathrm{m}^3$. What relationship between $t$ and $t_0$ is true?
The displacement y of a particle in a medium can be expressed as $y=10^{-6} \sin (110 t+20 x+\pi / 4) m$, where $t$ is in seconds and $x$ in meter. The speed of the wave is
The displacement $y$ of a wave travelling in the $x$-direction is given by $y=10^{-4} \sin \left(600 t-2 x+\frac{\pi}{3}\right)$ metres where $\mathrm{x}$ is expressed in metres and $\mathrm{t}$ in seconds. The speed of the wave-motion, in $\mathrm{ms}^{-1}$, is
A mass $\mathrm{M}$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes SHM of time period T. If the mass is increased by $\mathrm{m}$, the time period becomes $\frac{5 \mathrm{~T}}{3}$. Then the ratio of $\frac{\mathrm{m}}{\mathrm{M}}$ is
The displacement of a particle varies according to the relation $x=4(\cos \pi t+\sin \pi t)$. The amplitude of the particle is
Two particles $\mathrm{A}$ and $\mathrm{B}$ of equal masses are suspended from two massless springs of spring constant $\mathrm{k}_1$ and $\mathrm{k}_2$, respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of $A$ and $B$ is
A tuning fork of known frequency $256 \mathrm{~Hz}$ makes 5 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was
A body executes simple harmonic motion. The potential energy (P.E), the kinetic energy (K.E) and total energy (T.E) are measured as a function of displacement $x$. Which of the following statements is true?
A child swinging on a swing in sitting position, stands up, then the time period of the swing will
In a simple harmonic oscillator, at the mean position
A tuning fork arrangement (pair) produces 4 beats / sec with one fork of frequency $288 \mathrm{cps}$. A little wax is placed on the unknown fork and it then produces 2 beats /sec. The frequency of the unknown fork is
Tube A has both ends open while tube B has one end closed, otherwise they are identical. The ratio of fundamental frequency of tube $A$ and $B$ is