A particle is executing SHM along a straight line. Its velocities at distances $x_1$ and $x_2$ from the mean position are $V_1$ and $V_2,$ respectively. Its time period is

A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is:

Two cars moving in opposite directions approach each other with speed of 22 m/s and 16.5 m/s, respectively. The driver of the first car blows a horn having a frequency 400 Hz. The frequency heard by the driver of the second car is (velocity of sound: 340 m/s)

A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is $20$ m/s$^2$ at a distance of $5$ m from the mean position. The time period of oscillation is

The displacement of a particle executing simple harmonic motion is given by $y = A_0 + A \sin \omega t + B \cos \omega t.$ Then the amplitude of its oscillation is given by:

Average velocity of a particle executing SHM in one complete vibration is:

The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the figure. The y-projection of the radius vector of rotating particle P is:

The phase difference between displacement and acceleration of a particle in a simple harmonic motion is:

A spring is stretched by $5$ cm by a force of $10$ N. The time period of the oscillations when a mass of $2$ kg is suspended by it is:

A body is executing simple harmonic motion with frequency $n,$ the frequency of its potential energy is:

Two pendulums of length $121 cm$ and $100 cm$ start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean position is:

The potential energy of a long spring when stretched by 2 cm is $U.$ If the spring is stretched by 8 cm, potential energy stored in it will be:

The $x-t$ graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at $t = 2s$ is:

If $x = 5 \sin\left(\pi t + \frac{\pi}{3}\right)$ represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are:

If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is $\frac{x}{2}$ times its original time period. Then the value of $x$ is: