The displacement of a particle executing SHM | vedclass

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

Question

(B) The displacement equation for a particle executing $SHM$ is given by $x = A \sin(\omega t + \phi)$.Comparing the given equation $x = 3 \sin \left(

Vedclass · Accepted Answer

$3 \ m, 6 \pi \ m/s$

Vedclass · Answer

(B) The displacement equation for a particle executing $SHM$ is given by $x = A \sin(\omega t + \phi)$.Comparing the given equation $x = 3 \sin \left(2 \pi t + \frac{\pi}{4}ight)$ with the standard form:Amplitude $A = 3 \ m$.Angular frequency $\omega = 2 \pi \ rad/s$.The maximum speed $v_{\max}$ of a particle in $SHM$ is given by the formula $v_{\max} = \omega A$.Substituting the values: $v_{\max} = (2 \pi \ rad/s) 	imes (3 \ m) = 6 \pi \ m/s$.Thus,the amplitude is $3 \ m$ and the maximum speed is $6 \pi \ m/s$.

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:

Similar Questions

$A$ point mass of $400 \, g$ executes $S.H.M.$ under a force $F = -(10 \, N m^{-1}) x$. If it crosses the centre of oscillation with a speed of $10 \, m s^{-1}$, the amplitude of motion is (in $ \, m$)

$A$ particle is executing the motion $x = A \cos (\omega t - \theta)$. The maximum velocity of the particle is

Two identical pendulums oscillate with a constant phase difference $\frac{\pi}{4}$ and same amplitude. If the maximum velocity of one is $v$,the maximum velocity of the other will be ........

The maximum velocity and the maximum acceleration of a body moving in a simple harmonic oscillator are $2 \ m/s$ and $4 \ m/s^2$,respectively. Then the angular velocity will be ..... $rad/s$.

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module