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Two massless springs with spring constants \( 2k \) and \( 9k \), carry \( 50 \ \text{g} \) and \( 100 \ \text{g} \) masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be:

Two waves executing simple harmonic motions travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the \( \sqrt{3} \) times of amplitude of individual motions. The phase difference between the two motions is __________ (degree).

When a particle executes Simple Harmonic Motion, the nature of graph of velocity as a function of displacement will be:

Time period of a simple pendulum in a stationary lift is ' \( T \)'. If the lift acceleration with \( \frac{g}{6} \) vertically upwards then the time period will be: (where \( g \) = acceleration due to gravity)

The motion of a simple pendulum executing S.H.M. is represented by the following equation.

\( y = A \sin(\pi t + \phi) \), where time is measured in second. The length of pendulum is:

The equation of a particle executing simple harmonic motion is given by \( x = \sin \!\pi \left( t + \frac{1}{3} \right) ) \, \text{m} \). At \( t = 1 \, \text{s} \), the speed of particle will be (Given : \( \pi = 3.14 \) ).

As per given figures, two springs of spring constants \( k \) and \( 2k \) are connected to mass \( m \). If the period of oscillation in figure (a) is \( 3 \, \text{s} \), then the period of oscillation in figure (b) will be \( \sqrt{x} \, \text{s} \). The value of \( x \) is __________.

The metallic bob of simple pendulum has the relative density \( 5 \). The time period of this pendulum is \( 10\,\text{s} \). If the metallic bob is immersed in water, then the new time period becomes \( 5\sqrt{x}\,\text{s} \). The value of \( x \) will be _____.

A particle executes simple harmonic motion. Its amplitude is \( 8 \, \text{cm} \) and time period is \( 6 \, \text{s} \). The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is ________ \( \text{s} \).

Two identical positive charges \( Q \) each are fixed at a distance of '\( 2a \)' apart from each other. Another point charge \( q_0 \) with mass ‘\( m \)’ is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge \( q_0 \) executes SHM. The time period of oscillation of charge \( q_0 \) will be:

A body is performing simple harmonic with an amplitude of \( 10 \, \text{cm} \). The velocity of the body was tripled by air Jet when it is at \( 5 \, \text{cm} \) from its mean position. The new amplitude of vibration is \( \sqrt{x} \) cm. The value of \( x \) is __________.

The displacement of simple harmonic oscillator after \( 3 \, \text{seconds} \) starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is:

The potential energy of a particle of mass \( 4 \, \text{kg} \) in motion along the \( x \)-axis is given by \( U = 4(1 - \cos 4x) \, \text{J} \). The time period of the particle for small oscillation \( (\sin \theta \simeq \theta) \) is \( \left( \dfrac{\pi}{K} \right) \, \text{s} \). The value of \( K \) is __________.

In figure (A), mass \( 2m \) is fixed on mass \( m \) which is attached to two springs of spring constant \( k \). In figure (B), mass \( m \) is attached to two springs of spring constant \( k \) and \( 2k \). If mass \(m\) in (A) and (B) are displaced by distance \( x \) horizontally and then released, then time period \( T_1 \) & \( T_2 \) corresponding to (A) and (B) respectively follow the relation.

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JEE Main 2022 27th June Morning Shift

The displacement of simple harmonic oscillator after \( 3 \, \text{seconds} \) starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is: