When a particle of mass m is attached to a vertical spring of spring constant k and released, its mo

English

Gujarati

Hindi

13.Oscillations

hard

When a particle of mass $m$ is attached to a vertical spring of spring constant $k$ and released, its motion is described by $y ( t )= y _{0} \sin ^{2} \omega t ,$ where $'y'$ is measured from the lower end of unstretched spring. Then $\omega$ is

A

$\sqrt{\frac{g}{y_{0}}}$

B

$\sqrt{\frac{g}{2 y_{0}}}$

C

$\frac{1}{2} \sqrt{\frac{g}{y_{0}}}$

D

$\sqrt{\frac{2 g}{y_{0}}}$

(JEE MAIN-2020)

Solution

$y = y _{0} \sin ^{2} \omega t$

$y =\frac{ y _{0}}{2}(1-\cos 2 \omega t )$

$y -\frac{ y _{0}}{2}=-\frac{ y _{0}}{2} cos 2 \omega t$

Amplitude : $\frac{y_{0}}{2}$

$\frac{y_{0}}{2}=\frac{m g}{K}$

$2 \omega=\sqrt{\frac{K}{m}}=\sqrt{\frac{2 g}{y_{0}}}$

$\omega=\sqrt{\frac{g}{2 y_{0}}}$

Standard 11

Physics

Share

Similar Questions

Is the following Statement True or False ?

$1.$ If the spring is cut in two equal piece the spring constant of every piece decreases.

$2.$ Displacement of $SHO$ increases, its acceleration decrease.

$3.$ A system can happen to oscillate, have more than one natural frequency.

$4.$ The periodic time of $SHM$ depend on amplitude or energy or phase constant.

medium

Two bodies $M$ and $N $ of equal masses are suspended from two separate massless springs of force constants $k_1$ and $k_2$ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude $M$ to that of $N$ is

medium

(IIT-1988)

Two springs, of force constants $k_1$ and $k_2$ are connected to a mass $m$ as shown. The frequency of oscillation of the mass is $f$ If both $k_1$ and $k_2$ are made four times their original values, the frequency of oscillation becomes

medium

(AIEEE-2007)

A mass m performs oscillations of period $T$ when hanged by spring of force constant $K$. If spring is cut in two parts and arranged in parallel and same mass is oscillated by them, then the new time period will be

medium

Four massless springs whose force constants are $2k, 2k, k$ and $2k$ respectively are attached to a mass $M$ kept on a frictionless plane (as shown in figure). If the mass $M$ is displaced in the horizontal direction, then the frequency of oscillation of the system is

medium