The equation of a particle executing simple h | vedclass

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

Question

(B) The given equation is $x = \sin \pi (t + 1/3) \, m$.Expanding the equation,we get $x = \sin (\pi t + \pi/3) \, m$.The velocity $v$ is the derivati

Vedclass · Accepted Answer

$157$

Vedclass · Answer

(B) The given equation is $x = \sin \pi (t + 1/3) \, m$.Expanding the equation,we get $x = \sin (\pi t + \pi/3) \, m$.The velocity $v$ is the derivative of displacement $x$ with respect to time $t$:$v = \frac{dx}{dt} = \frac{d}{dt} [\sin (\pi t + \pi/3)] = \pi \cos (\pi t + \pi/3) \, m/s$.At $t = 1 \, s$:$v = \pi \cos (\pi(1) + \pi/3) = \pi \cos (4\pi/3) \, m/s$.Since $\cos (4\pi/3) = \cos (\pi + \pi/3) = -\cos (\pi/3) = -1/2$:$v = \pi 	imes (-1/2) = -\pi/2 \, m/s$.The speed is the magnitude of velocity:$|v| = |-\pi/2| = \pi/2 \, m/s$.Converting to $cm/s$ $(1 \, m = 100 \, cm)$:$|v| = (\pi/2) 	imes 100 = 50\pi \, cm/s$.Given $\pi = 3.14$:$|v| = 50 	imes 3.14 = 157 \, cm/s$.

The equation of a particle executing simple harmonic motion is given by $x = \sin \pi (t + 1/3) \, m$. At $t = 1 \, s$,the speed of the particle will be .......... $cm \, s^{-1}$ (Given: $\pi = 3.14$)

Similar Questions

$A$ particle is performing simple harmonic motion with amplitude $A$ and angular velocity $\omega$. The ratio of maximum velocity to maximum acceleration is

$A$ spring executes $S.H.M.$ with mass $10 \ kg$ attached to it. The force constant of the spring is $10 \ N/m$. If at any instant its velocity is $40 \ cm/s$,the displacement at that instant is (Amplitude of $S.H.M.$ $= 0.5 \ m$) (in $m$)

$A$ particle performing $SHM$ has a time period of $\frac{2 \pi}{\sqrt{3}} \,s$ and a path length of $4 \,cm$. The displacement from the mean position at which the magnitude of acceleration is equal to the magnitude of velocity is (in $\,cm$)

Write the formula for the instantaneous velocity of a particle performing $SHM$ along the $X$-axis.

Maximum velocity and maximum acceleration of a particle executing $SHM$ are $\beta$ and $\alpha$ respectively. What will be its frequency?

Vedclass Test Series

Exam Paper Generator

Online Exam Module