The displacement of a particle executing SHM | vedclass

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

Question

(C) The displacement of the particle is given by the equation: $y = A \sin(\omega t)$,where $A$ is the amplitude and $\omega$ is the angular frequency

Vedclass · Accepted Answer

$50$

Vedclass · Answer

(C) The displacement of the particle is given by the equation: $y = A \sin(\omega t)$,where $A$ is the amplitude and $\omega$ is the angular frequency.Comparing this with the given equation $y = 0.25 \sin(200t)$:Amplitude $A = 0.25 \ cm$Angular frequency $\omega = 200 \ rad \ s^{-1}$The velocity $v$ of the particle is the time derivative of displacement:$v = \frac{dy}{dt} = \frac{d}{dt} [0.25 \sin(200t)] = 0.25 	imes 200 \cos(200t) = 50 \cos(200t)$The maximum speed $v_{max}$ occurs when $\cos(200t) = 1$:$v_{max} = A \omega = 0.25 	imes 200 = 50 \ cm \ s^{-1}$.

The displacement of a particle executing $SHM$ is given by $y = 0.25 \sin(200t) \ cm$. The maximum speed of the particle is $......... \ cm \ s^{-1}$.

Similar Questions

$A$ particle starts $S.H.M.$ from the mean position as shown in the figure. Its amplitude is $A$ and its time period is $T$. At a certain instant,its speed is half of its maximum speed. What is its displacement at this instant?

The equations for the displacements of two particles in simple harmonic motion are $y_1=0.1 \sin \left(100 \pi t+\frac{\pi}{3}\right)$ and $y_2=0.1 \cos \pi t$ respectively. The phase difference between the velocities of the two particles at a time $t=0$ is

The maximum velocity of a simple harmonic motion represented by $y = 3\sin \left( 100t + \frac{\pi}{6} \right)$ is given by

$A$ particle performs linear $S.H.M.$ When the displacement of the particle from the mean position is $3 \ cm$ and $4 \ cm$,the corresponding velocities are $8 \ cm/s$ and $6 \ cm/s$ respectively. Its periodic time is

The velocity of a particle executing a simple harmonic motion is $13 \ m/s$, when its distance from the equilibrium position $(Q)$ is $3 \ m$ and its velocity is $12 \ m/s$, when it is $5 \ m$ away from $Q$. The frequency of the simple harmonic motion is

Vedclass Test Series

Exam Paper Generator

Online Exam Module