A body is in simple harmonic motion with a ti | vedclass

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

Question

(C) Given: Time period,$T = 0.5 \ s$. Amplitude,$A = 1 \ cm$.The displacement of a particle in simple harmonic motion starting from the mean position

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(C) Given: Time period,$T = 0.5 \ s$. Amplitude,$A = 1 \ cm$.The displacement of a particle in simple harmonic motion starting from the mean position is given by $x = A \sin(\omega t)$.To reach a displacement of $x = A/2$,we have $A/2 = A \sin(\omega t)$,which implies $\sin(\omega t) = 1/2$.Thus,$\omega t = \pi/6$. Since $\omega = 2\pi/T$,we have $(2\pi/T) \cdot t = \pi/6$,which gives $t = T/12$.Substituting $T = 0.5 \ s$,the time taken is $t = 0.5 / 12 \ s$.The average velocity is defined as the total displacement divided by the total time taken.Average velocity $v_{avg} = \frac{\Delta x}{\Delta t} = \frac{A/2}{T/12} = \frac{1/2}{0.5/12} = \frac{0.5}{0.5/12} = 12 \ cm/s$.

$A$ body is in simple harmonic motion with a time period of $0.5 \ s$ and an amplitude of $1 \ cm$. Find the average velocity in the interval in which it moves from the equilibrium position to half of its amplitude (in $cm/s$).

Similar Questions

The amplitude and the periodic time of a $S.H.M.$ are $5 \, cm$ and $6 \, s$ respectively. At a distance of $2.5 \, cm$ away from the mean position,the phase will be

$A$ small mass executes linear $SHM$ about $O$ with amplitude $a$ and period $T.$ Its displacement from $O$ at time $T/8$ after passing through $O$ is:

The acceleration of a particle starting from rest varies with time according to the relation $A = -a\omega^2 \sin\omega t$. The displacement of this particle at a time $t$ will be

$A$ particle executes $SHM$ with an amplitude of $20 \, cm$ and a time period of $12 \, s$. What is the minimum time required for it to move between two points $10 \, cm$ on either side of the mean position?

$A$ particle executes simple harmonic motion (amplitude $= A$) between $x = -A$ and $x = +A$. The time taken for it to go from $x = 0$ to $x = A/2$ is ${T_1}$ and to go from $x = A/2$ to $x = A$ is ${T_2}$. Then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module