List of top Physics Questions on Waves and Oscillations

The time period of a simple harmonic oscillator is \[ T=2\pi\sqrt{\frac{m}{k}}. \] Measured value of mass \(m\) has an accuracy of \(10%\) and time for 50 oscillations of the spring is found to be \(60\,\text{s}\) using a watch of 2 s resolution. Percentage error in determination of spring constant \(k\) is:
The displacement of a particle executing simple harmonic motion with time period \(T\) is expressed as \[ x(t)=A\sin\omega t, \] where \(A\) is the amplitude of oscillation. If the maximum value of the potential energy of the oscillator is found at \[ t=\frac{T}{2\beta}, \] then the value of \(\beta\) is ________.
A cylindrical block of mass $M$ and area of cross section $A$ is floating in a liquid of density $\rho$ with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is ___.

Using a variable frequency ac voltage source the maximum current measured in the given LCR circuit is 50 mA for V = 5 sin (100t) The values of L and R are shown in the figure. The capacitance of the capacitor (C) used is_______ µF.

Using a simple pendulum experiment $g$ is determined by measuring its time period $T$. Which of the following plots represent the correct relation between the pendulum length $L$ and time period $T$?
A body of mass 2 kg is moving along x-direction such that its displacement as function of time is given by $x(t) = \alpha t^2 + \beta t + \gamma$ m, where $\alpha = 1$ m/s$^2$, $\beta = 1$ m/s and $\gamma = 1$ m. The work done on the body during the time interval $t = 2$ s to $t = 3$ s, is _________ J.
A simple pendulum of length $30$ cm makes $20$ oscillations in $10$ s on a certain planet. Another pendulum makes $40$ oscillations in $10$ s on the same planet. Find the length of the second pendulum.
During SHM, K.E. of particle in SHM varies with frequency of 176 Hz. Find the frequency of SHM of the particle.
A cylindrical body of mass m and cross section A is floating in a liquid of density $\rho_{L}$ such that its axis is vertical. If body is displaced by a small displacement 'x' vertically, find the time period of oscillation of the body :
A particle moves according to the equation x = Asin(\(\omega t\)). The potential energy is maximum at time \(t = \frac{T}{2\beta}\), where T is the time period of particle. Find the minimum value of \(\beta\) :

There are two spring–block systems as shown. They are in equilibrium. If $\dfrac{m_1}{m_2}=\alpha$ and $\dfrac{k_1}{k_2}=\beta$, then the ratio of the energies of the springs $\left(\dfrac{E_1}{E_2}\right)$ is:

Two mechanical waves on strings of equal length (\( L \)) and tension (\( T \)) having linear mass density \( \mu_1/\mu_2 = 1/2 \). Find the ratio of time taken for a wave pulse to travel from one end to the other in both strings. (Ignore gravity)
Detector \( D \) moves from \( A \) to \( B \) and observes the frequencies are differing by 10 Hz. The source is emitting frequency \( f_0 \) as shown: Speed of detector is 35 times less than speed of sound. Then \( f_0 \) is.
Statement–I: Time period of a simple pendulum increases if the mass of the bob is increased.
Statement–II: Time period of a simple pendulum depends only on its length and acceleration due to gravity.
System is released after slightly stretching it. Find angular frequency of its oscillations:
A simple pendulum has a length of $ L = 2 \, \text{m} $. What is the time period of the pendulum? (Assume $ g = 9.8 \, \text{m/s}^2 $)

In an oscillating spring mass system, a spring is connected to a box filled with sand. As the box oscillates, sand leaks slowly out of the box vertically so that the average frequency ω(t) and average amplitude A(t) of the system change with time t. Which one of the following options schematically depicts these changes correctly? 

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). 
Assertion (A): Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain. 
Reason (R): Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa. In the light of the above statements. 
choose the most appropriate answer from the options given below:

Two bodies A and B of equal mass are suspended from two massless springs of spring constant \( k_1 \) and \( k_2 \), respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the maximum velocity of B is:
An audio transmitter (T) and a receiver (R) are hung vertically from two identical massless strings of length 8 m with their pivots well separated along the $X$ axis. They are pulled from the equilibrium position in opposite directions along the $X$ axis by a small angular amplitude $\theta_0 = \cos^{-1}(0.9)$ and released simultaneously. If the natural frequency of the transmitter is 660 Hz and the speed of sound in air is 330 m/s, the maximum variation in the frequency (in Hz) as measured by the receiver (Take the acceleration due to gravity $g = 10\, \text{m/s}^2$) is ___

As shown in the figures, a uniform rod $ OO' $ of length $ l $ is hinged at the point $ O $ and held in place vertically between two walls using two massless springs of the same spring constant. The springs are connected at the midpoint and at the top-end $ (O') $ of the rod, as shown in Fig. 1, and the rod is made to oscillate by a small angular displacement. The frequency of oscillation of the rod is $ f_1 $. On the other hand, if both the springs are connected at the midpoint of the rod, as shown in Fig. 2, and the rod is made to oscillate by a small angular displacement, then the frequency of oscillation is $ f_2 $. Ignoring gravity and assuming motion only in the plane of the diagram, the value of $\frac{f_1}{f_2}$ is:

The center of a disk of radius $ r $ and mass $ m $ is attached to a spring of spring constant $ k $, inside a ring of radius $ R>r $ as shown in the figure. The other end of the spring is attached on the periphery of the ring. Both the ring and the disk are in the same vertical plane. The disk can only roll along the inside periphery of the ring, without slipping. The spring can only be stretched or compressed along the periphery of the ring, following Hooke’s law. In equilibrium, the disk is at the bottom of the ring. Assuming small displacement of the disc, the time period of oscillation of center of mass of the disk is written as $ T = \frac{2\pi}{\omega} $. The correct expression for $ \omega $ is ( $ g $ is the acceleration due to gravity): 

A pendulum completes 20 oscillations in 40 seconds. What is its frequency?
The force of gravitation between two bodies does not depend on:
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 velocities are the same, the ratio of the amplitude of P to the amplitude of Q is :