Velocity at mean position of a particle executing $S.H.M.$ is $v$, they velocity of the particle at a distance equal to half of the amplitude
A$4v$
B$2v$
C$\frac{{\sqrt 3 }}{2}v$
D$\frac{{\sqrt 3 }}{4}v$
Easy
Download our app for free and get started
C$\frac{{\sqrt 3 }}{2}v$
c (c) Velocity in mean position $v = a\omega ,$ velocity at a distance of half amplitude.
$v' = \omega \sqrt {{a^2} - {y^2}} $
$ = \omega \sqrt {{a^2} - \frac{{{a^2}}}{4}} $
$ = \sqrt {\frac{3}{2}} \,a\omega $
$= \sqrt {\frac{3}{2}} \,v$
Download our app
and get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
A particle is performing simple harmonic motion with amplitude A and angular velocity ${\omega }$. The ratio of maximum velocity to maximum acceleration is
A cylindrical block of density $\rho$ is partially immersed in a liquid of density $3\rho .$ The plane surface of the block remains parallel to the surface of the liquid. The height of the block is $60\, cm.$ The block performs $SHM$ when displaced from its mean position. [Use $ g = 9.8\, m/s^2$]
A brass cube of side $a$ and density $\rho$ is floating in mercury of density $\sigma$. If the cube is displaced a bit vertically, it executes $S.H.M.$ Its time period will be
If $< E >$ and $< U >$ denote the average kinetic and the average potential energies respectively of mass describing a simple harmonic motion, over one period, then the correct relation is
A $3\ kg$ sphere dropped through air has a terminal speed of $25\ m/s$. (Assume that the drag force is $-bv$.) Now suppose the sphere is attached to a spring of force constant $k = 300\ N/m$, and that it oscillates with an initial amplitude of $20\ cm$. What is the angular frequencu of its damped $SHM$? ..... $rad/s$