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 amplitude of a particle executing $S.H.M.$ with a frequency of $60 \, Hz$ is $0.01 \, m$. The maximum value of the acceleration of the particle is

The acceleration $a$ of a particle undergoing $S.H.M.$ is shown in the figure. Which of the labelled points corresponds to the particle being at $-x_{max}$?

Write the formula of instantaneous acceleration of $SHM$ particle along $X$-axis.

$A$ particle is performing $S.H.M.$ starting from the extreme position. The graphical representation shows that between displacement and acceleration,there is a phase difference of:

What is restoring force?

Vedclass Test Series

Exam Paper Generator

Online Exam Module