Which one of the following equations of motio | vedclass

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

Question

(C) The defining condition for Simple Harmonic Motion $(S.H.M.)$ is that the acceleration $(a)$ is directly proportional to the negative of the displa

Vedclass · Accepted Answer

$Acceleration = -k(x+a)$

Vedclass · Answer

(C) The defining condition for Simple Harmonic Motion $(S.H.M.)$ is that the acceleration $(a)$ is directly proportional to the negative of the displacement $(x)$ from the mean position.Mathematically,this is expressed as $a = -\omega^2 x$,where $\omega$ is the angular frequency.In option $(C)$,the equation is $a = -k(x+a)$. If we define a new coordinate $x' = x+a$,then the equation becomes $a = -k x'$.This represents an $S.H.M.$ about the equilibrium position $x = -a$.Since the acceleration is proportional to the displacement from the mean position and directed towards it,option $(C)$ correctly represents $S.H.M.$

Which one of the following equations of motion represents simple harmonic motion? (Where $k, k_0, k_1$ and $a$ are all positive constants)

Similar Questions

How many amplitudes does a Simple Harmonic Oscillator $(SHO)$ cover in half of its time period?

If the displacement equation of a particle is represented by $y = A\sin PT + B\cos PT$,the particle executes

$A$ simple harmonic wave having an amplitude $a$ and time period $T$ is represented by the equation $y = 5 \sin \pi (t + 4) \ m$. Then the value of amplitude $(a)$ in $(m)$ and time period $(T)$ in seconds are:

$A$ system exhibiting $S.H.M.$ must possess

The function $x = A \sin^2 \omega t + B \cos^2 \omega t + C \sin \omega t \cos \omega t$ does not represent $SHM$ for which of the following conditions?

Vedclass Test Series

Exam Paper Generator

Online Exam Module