Waves & Oscillations PYQ — Page 8

The phase difference between two points separated by 1 m on a wave of wavelength 4 m is:

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 ? 

Two travelling waves produces a standing wave represented by equation. $y=(1.0\mathrm{mm})\mathrm{cos}[(1.57{\mathrm{cm}}^{-1})x]\mathrm{sin}[(78.5{s}^{-1})t]$. The node closest to the origin in the region $x>0$ will be at $x=......(\text{in}\mathrm{cm}).$

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

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.

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 ________.

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

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:

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 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:

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by $4%$, will be ___ $%$.

A closed organ pipe of length $L$ and an open organ pipe contain gases of densities ${\rho }_{1}$ and ${\rho }_{2}$ respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is $\frac{x}{3}L\sqrt{\frac{{\rho }_{1}}{{\rho }_{2}}}$, where $x$ is _______. (Round off to the Nearest Integer)

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.

Two identical springs of spring constant $2k$ are attached to a block of mass $m$ and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this system is : 

A block of mass $1\mathrm{kg}$ attached to a spring is made to oscillate with an initial amplitude of $12\mathrm{cm}$. After $2$ minutes the amplitude decreases to $6\mathrm{cm}$. Determine the value of the damping constant for this motion. (take $\mathrm{ln}2=0.693$ )

When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is:

Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance $\frac{R}{2}$ from the earth's centre, where $R$ is the radius of the earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period:

$Y=A\mathrm{sin}(\omega t+{\phi }_{0})$ 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:

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:

${T}_{0}$ is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to $\frac{1}{16}$ times of its initial value, the modified time period is