If the maximum velocity and maximum accelerat | vedclass

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

Question

(C) For a particle executing $SHM$,the maximum velocity is given by $V_{\max} = \omega A$,where $\omega$ is the angular frequency and $A$ is the ampli

Vedclass · Accepted Answer

$6.28$

Vedclass · Answer

(C) For a particle executing $SHM$,the maximum velocity is given by $V_{\max} = \omega A$,where $\omega$ is the angular frequency and $A$ is the amplitude.The maximum acceleration is given by $a_{\max} = \omega^2 A$.According to the problem,the magnitudes are equal: $V_{\max} = a_{\max}$.Substituting the expressions: $\omega A = \omega^2 A$.Dividing both sides by $\omega A$ (assuming $A 
eq 0$ and $\omega 
eq 0$),we get $\omega = 1 	ext{ rad/s}$.The time period $T$ is given by $T = \frac{2\pi}{\omega}$.Substituting $\omega = 1$,we get $T = 2\pi \approx 2 	imes 3.14 = 6.28 	ext{ s}$.

If the maximum velocity and maximum acceleration of a particle executing $SHM$ are equal in magnitude,the time period will be .... $\sec$

Similar Questions

$A$ long stiff uniform wire of length $\ell$ is suspended from one end. The time period of oscillations of the wire is $T$. If the wire is now bent into a circle and suspended from a knife edge so that it can oscillate freely in the plane of the ring,its time period will be

$A$ body performs $S.H.M.$ under the action of force $F_1$ with period $T_1$ seconds. If the force is changed to $F_2$,it performs $S.H.M.$ with period $T_2$ seconds. If both forces $F_1$ and $F_2$ act simultaneously in the same direction on the body,the period in seconds will be

$A$ large horizontal surface moves up and down in $S.H.M.$ with an amplitude of $1 \, cm$. If a mass of $10 \, kg$ placed on the surface is to remain continuously in contact with it,the maximum frequency of $S.H.M.$ will be .... $Hz$.

$A$ uniform disc of mass $M$ and radius $R$ is suspended in a vertical plane from a point on its periphery. Its time period of oscillation is ........

$A$ particle is executing a simple harmonic motion. Its maximum acceleration is $\alpha$ and maximum velocity is $\beta$. Then,its time period of vibration will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module