JEE Main Physics — Waves & Oscillations previous year questions with solutions.
$Y=A\mathrm{sin}(\omega t+{\phi }_{0})$ is the time-displacement equation of a $SHM.$ At $t=0$ the displacement of the particle is $Y=\frac{A}{2}$ and it is moving along negative $x$-direction. Then the initial phase angle ${\phi }_{0}$ will be:
The amplitude of wave disturbance propagating in the positive $x$-direction is given by $y=\frac{1}{(1+x{)}^{2}}$ at time $t=0$ and $y=\frac{1}{1+(x-2{)}^{2}}$ at $t=1s$, where $x$ and $y$ are in metres. The shape of wave does not change during the propagation. The velocity of the wave will be $m{s}^{-1}.$
For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?
The phase difference between two points separated by 1 m on a wave of wavelength 4 m is:
A wire having a linear mass density $9.0\times {10}^{-4}\mathrm{kg}{m}^{-1}$ is stretched between two rigid supports with a tension of $900N.$ The wire resonates at a frequency of $500\mathrm{Hz}.$ The next higher frequency at which the same wire resonates is $550\mathrm{Hz}.$ The length of the wire is ___________ $m.$
A mass of $5\mathrm{kg}$ is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length $4m$ has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed ? 
A particle starts executing simple harmonic motion $(\mathrm{SHM})$ of amplitude $a$ and total energy $E.$ At any instant, its kinetic energy is $\frac{3E}{4}$, then its displacement $y$ is given by:
For a body executing S.H.M. : (a) Potential energy is always equal to its $K.E.$ (b) Average potential and kinetic energy over any given time interval are always equal. (c) Sum of the kinetic and potential energy at any point of time is constant. (d) Average $K.E.$ in one time period is equal to average potential energy in one time period. Choose the most appropriate option from the options given below :
Two simple harmonic motion, are represented by the equations ${y}_{1}=10\mathrm{sin}(3\pi t+\frac{\pi }{3});{y}_{2}=5(\mathrm{sin}3\pi t+\sqrt{3}\mathrm{cos}3\pi t)$ Ratio of amplitude of ${y}_{1}$ to ${y}_{2}=x:1$. The value of $x$ is
A particle of mass $1\mathrm{kg}$ is hanging from a spring of force constant $100N{m}^{-1}.$ The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period $T.$ The time when the kinetic energy and potential energy of the system will become equal, is $\frac{T}{n}.$ The value of $n$ is ________.
Two simple harmonic motions are represented by the equations ${x}_{1}=5\mathrm{sin}(2\pi t+\frac{\pi }{4})$ and ${x}_{2}=5\sqrt{2}(\mathrm{sin}2\pi t+\mathrm{cos}2\pi t).$ The amplitude of the second motion is _____ times the amplitude in the first motion.
In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.
The function of time representing a simple harmonic motion with a period of $\frac{\pi }{\omega }$ is :
Consider two identical springs each of spring constant $k$ and negligible mass compared to the mass $M$ as shown. Fig. $1$ shows one of them and Fig. $2$ shows their series combination. The ratios of time period of oscillation of the two SHM is $\frac{{T}_{b}}{{T}_{a}}=\sqrt{x},$ where value of $x$ is ______. (Round off to the Nearest Integer) 
A particle executes S.H.M. with amplitude $A$ and time period $T$. The displacement of the particle when its speed is half of maximum speed is $\frac{\sqrt{x}A}{2}.$ The value of $x$ is
The amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass $=500g$, Decay constant $=20g{s}^{-1}$ then how much time is required for the amplitude of the system to drop to half of its initial value? $(\mathrm{ln}2=0.693)$
Given below are two statements: Statement $I$: A second's pendulum has a time period of $1$ second. Statement $\mathrm{II}$: It takes precisely one second to move between the two extreme positions. In the light of the above statements, choose the correct answer from the options given below
A particle executes S.H.M., the graph of velocity as a function of displacement is :
If the time period of a two meter long simple pendulum is $2s$, the acceleration due to gravity at the place where pendulum is executing S.H.M. is:
When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is:
A $25m$ long antenna is mounted on an antenna tower. The height of the antenna tower is $75m$. The wavelength (in meter) of the signal transmitted by this antenna would be :
A student is performing the experiment of the resonance column. The diameter of the column tube is $6\mathrm{cm}$. The frequency of the tuning fork is $504\mathrm{Hz}$. Speed of the sound at the given temperature is $336m{s}^{-1}$. The zero of the meter scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is:
The point $A$ moves with a uniform speed along the circumference of a circle of radius $0.36m$ and covers $30^{\circ}$ in $0.1s$. The perpendicular projection $P$ from $A$ on the diameter $MN$ represents the simple harmonic motion of $P$. The restoration force per unit mass when $P$ touches $M$ will be : 
A particle executes simple harmonic motion represented by displacement function as $x(t)=A\mathrm{sin}(\omega t+\phi )$. If the position and velocity of the particle at $t=0s$ are $2\mathrm{cm}$ and $2\omega \mathrm{cm}{s}^{-1}$ respectively, then its amplitude is $x\sqrt{2}\mathrm{cm}$ where the value of $x$ is