A particle is in a linear SHM. If the acceleration and the corresponding velocity of this particle are ' a ' and ' v ', then the graph relating to these values is

Question

A particle is in a linear SHM. If the acceleration and the corresponding velocity of this particle are ' a ' and ' v ', then the graph relating to these values is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

The equation giving relation between acceleration and speed as function of distance from mean position
is

a = - ω^{2} x

.....(i)

v = ω a^{2} - x^{2}

.....(ii)
from equation (i) and (ii) we get

a^{2} = ω^{4} (A^{2} - \frac{v ^{2}}{ω ^{2}})

Q. A particle is in a linear SHM. If the acceleration and the corresponding velocity of this particle are ' a ' and ' v ', then the graph relating to these values is

The equation giving relation between acceleration and speed as function of distance from mean position is a=−ω2x .....(i) v=ωa2−x2​ .....(ii) from equation (i) and (ii) we get a2=ω4(A2−ω2v2​)

Q. A particle is in a linear SHM. If the acceleration and the corresponding velocity of this particle are ' $a$ ' and ' $v$ ', then the graph relating to these values is

The equation giving relation between acceleration and speed as function of distance from mean position
is $a = - ω^{2} x$ .....(i)
$v = ω a^{2} - x^{2}$ .....(ii)
from equation (i) and (ii) we get
$a^{2} = ω^{4} (A^{2} - \frac{v ^{2}}{ω ^{2}})$