Which of the following statements is correct | vedclass

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

Question

(A) In $S.H.M.$,the displacement is given by $x = A \sin(\omega t)$.Velocity is the derivative of displacement with respect to time: $v = \frac{dx}{dt

Vedclass · Accepted Answer

Velocity leads the displacement by a phase of $\frac{\pi}{2}$ radians.

Vedclass · Answer

(A) In $S.H.M.$,the displacement is given by $x = A \sin(\omega t)$.Velocity is the derivative of displacement with respect to time: $v = \frac{dx}{dt} = A\omega \cos(\omega t) = A\omega \sin(\omega t + \frac{\pi}{2})$.Comparing the phases,the velocity leads the displacement by a phase of $\frac{\pi}{2}$ radians.Acceleration is the derivative of velocity with respect to time: $a = \frac{dv}{dt} = -A\omega^2 \sin(\omega t) = A\omega^2 \sin(\omega t + \pi)$.Comparing the phases,the acceleration leads the displacement by a phase of $\pi$ radians (or lags by $\pi$ radians).Therefore,the correct statement is that velocity leads the displacement by a phase of $\frac{\pi}{2}$ radians.

Which of the following statements is correct for $S.H.M.$?

Similar Questions

$A$ particle executes $SHM$ with a period of $1.2 \, s$ and an amplitude of $8 \, cm$. Find the time it takes to travel $3 \, cm$ from the positive extremity of its oscillation.

The displacement of a simple harmonic oscillator after $3 \; s$ starting from its mean position is equal to half of its amplitude. The time period of the harmonic motion is $\dots \; s$.

$A$ particle is performing simple harmonic motion with an amplitude of $4 \, cm$ and a time period of $12 \, s$. What is the ratio of the time taken by the particle to travel from its mean position to $2 \, cm$ to the time taken to travel from $2 \, cm$ to its extreme position?

$A$ particle performs simple harmonic motion with a period of $2 \ s$. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is $\frac{1}{a} \ s$. The value of $a$ to the nearest integer is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module