Which of the following quantities is always n | vedclass

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

Question

(B) In $SHM$,the acceleration $\vec a$ is given by $\vec a = -\omega^2 \vec r$,where $\vec r$ is the displacement vector from the equilibrium position

Vedclass · Accepted Answer

$\vec a \cdot \vec r$

Vedclass · Answer

(B) In $SHM$,the acceleration $\vec a$ is given by $\vec a = -\omega^2 \vec r$,where $\vec r$ is the displacement vector from the equilibrium position.Taking the dot product of $\vec a$ and $\vec r$:$\vec a \cdot \vec r = (-\omega^2 \vec r) \cdot \vec r = -\omega^2 |\vec r|^2$.Since $\omega^2$ is always positive and $|\vec r|^2$ is always non-negative,the product $\vec a \cdot \vec r$ is always negative (except at the equilibrium position where it is zero).Therefore,the correct option is $B$.

Which of the following quantities is always negative in a $SHM$?

Similar Questions

The weight suspended from a spring oscillates up and down. The acceleration of the weight will be zero at

$A$ simple harmonic oscillator has an amplitude of $0.5 \ m$ and a time period of $2 \ s$. What is the magnitude of acceleration when it is displaced from the mean position by $0.25 \ m$?

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

$A$ $0.10\, kg$ block oscillates back and forth along a horizontal surface. Its displacement from the origin is given by: $x = (10\,cm)\cos [(10\,rad/s)\,t + \pi /2\,rad]$. What is the maximum acceleration experienced by the block?

Vedclass Test Series

Exam Paper Generator

Online Exam Module