Answer

Verified

87.3k+ views

**Hint**In mechanics and physics, simple harmonic motion is a special type of periodic motion where the restoring force on the moving object is directly proportional to the object's displacement magnitude and acts towards the object's equilibrium position. It is vibratory motion in a system in which the restoring force is proportional to the displacement from equilibrium

**Step by step solution**

As it is Simple harmonic motion so the equation of motion will be

\[F = - kx\]

Or the equation can be written as

\[\dfrac{{vdv}}{{dx}} = - {\omega ^2}x\]

Now integrating the expression with boundary condition,

\[\int\limits_{{v_0}}^v {vdv} = - {\omega ^2}\int\limits_0^x {xdx} \]

After integrating the above equation we get

$\left[ {\dfrac{{{v^2}}}{2}} \right]_{{v_0}}^v = - {\omega ^2}\left[ {\dfrac{{{x^2}}}{2}} \right]_0^x$

Now we have to apply the limit in the above equation so we get

$\left[ {\dfrac{{{v^2}}}{2} - \dfrac{{v_0^2}}{2}} \right] = - {\omega ^2}\left[ {\dfrac{{{x^2}}}{2}} \right]$

Now we have to do further calculation then we get

$\dfrac{1}{2}\left[ {{v^2} - v_0^2} \right] = \dfrac{{ - {\omega ^2}{x^2}}}{2}$

Now after simplifying the above equation we get

$v = \sqrt {v{}_0^2 - {\omega ^2}{x^2}} $

**Hence the correct answer is option is (B)**

**Note**

A speed vector speaks to the pace of progress of the situation of an object.The greatness of a speed vector gives the speed of an article while the vector course gives its direction.Velocity vectors can be added or deducted by the standards of vector addition.In math and mechanics, a relocation is a vector whose length is the most limited good ways from the underlying to the last situation of a point P going through movement. It quantifies both the distance and direction of the net or total motion along a straight line from the initial position to the final position of the point trajectory. A displacement may be identified with the translation that maps the initial position to the final position.

Recently Updated Pages

Name the scale on which the destructive energy of an class 11 physics JEE_Main

Write an article on the need and importance of sports class 10 english JEE_Main

Choose the exact meaning of the given idiomphrase The class 9 english JEE_Main

Choose the one which best expresses the meaning of class 9 english JEE_Main

What does a hydrometer consist of A A cylindrical stem class 9 physics JEE_Main

A motorcyclist of mass m is to negotiate a curve of class 9 physics JEE_Main

Other Pages

A pilot in a plane wants to go 500km towards the north class 11 physics JEE_Main

A passenger in an aeroplane shall A Never see a rainbow class 12 physics JEE_Main

A circular hole of radius dfracR4 is made in a thin class 11 physics JEE_Main

The potential energy of a certain spring when stretched class 11 physics JEE_Main

The ratio of speed of sound in Hydrogen to that in class 11 physics JEE_MAIN

A roller of mass 300kg and of radius 50cm lying on class 12 physics JEE_Main