A particle executes S.H.M. of period frac{2 p | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given: Period $T = \frac{2 \pi}{\sqrt{3}} 	ext{ s}$, total path length $= 4 	ext{ cm}$.Amplitude $A = \frac{	ext{path length}}{2} = \frac{4}{2}

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(B) Given: Period $T = \frac{2 \pi}{\sqrt{3}} 	ext{ s}$, total path length $= 4 	ext{ cm}$.Amplitude $A = \frac{	ext{path length}}{2} = \frac{4}{2} = 2 	ext{ cm}$.Angular frequency $\omega = \frac{2 \pi}{T} = \frac{2 \pi}{2 \pi / \sqrt{3}} = \sqrt{3} 	ext{ rad/s}$.Magnitude of acceleration $a = \omega^2 |x|$ and magnitude of velocity $v = \omega \sqrt{A^2 - x^2}$.Given $v = a$, so $\omega \sqrt{A^2 - x^2} = \omega^2 |x|$.Squaring both sides: $\omega^2 (A^2 - x^2) = \omega^4 x^2$.Dividing by $\omega^2$: $A^2 - x^2 = \omega^2 x^2$.Substituting values: $2^2 - x^2 = (\sqrt{3})^2 x^2$.$4 - x^2 = 3x^2 \implies 4x^2 = 4 \implies x^2 = 1$.Thus, $x = 1 	ext{ cm}$.

$A$ particle executes $S.H.M.$ of period $\frac{2 \pi}{\sqrt{3}} \text{ s}$ along a straight line $4 \text{ cm}$ long. The displacement of the particle at which the velocity is numerically equal to the acceleration is (in $\text{ cm}$)

Similar Questions

If the maximum velocity and maximum acceleration of a particle executing simple harmonic motion are respectively $5 \,m \,s^{-1}$ and $10 \,m \,s^{-2}$, then the time period of oscillation of the particle is

The displacement of a particle executing $SHM$ is given by $x = 3 \sin \left(2 \pi t + \frac{\pi}{4}\right)$,where $x$ is in $m$ and $t$ is in $s$. The amplitude and maximum speed of the particle are:

$A$ particle executing simple harmonic motion starts from the mean position with amplitude $A$ and periodic time $T$. At what displacement is its speed one-fourth of the maximum speed?

The velocity vector $v$ and displacement vector $x$ of a particle executing $SHM$ are related as $\frac{v dv}{dx} = -\omega^2 x$ with the initial condition $v = v_0$ at $x = 0$. The velocity $v$,when displacement is $x$,is

$A$ 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

Vedclass Test Series

Exam Paper Generator

Online Exam Module