A particle executes S.H.M with amplitude 'a' and time period T. The displacement of the particle when its speed is half of maximum speed is (√x a/2). The value of x is .

Question

A particle executes S.H.M with amplitude 'a' and time period T. The displacement of the particle when its speed is half of maximum speed is (√x a/2). The value of x is . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Fora particle executes S.H.M V=ω √a2 - x2 Given V=(Vmax/2)⇒ (a ω /2) (a2 ω 2/4)=ω 2a2-ω 2x2 x=(√3/2)a

Q. A particle executes S.H.M with amplitude $^{'} a^{'}$ and time period $T .$ The displacement of the particle when its speed is half of maximum speed is $\frac{x a}{2} .$ The value of $x$ is ____________ .

Fora particle executes S.H.M
$V = ω a^{2} - x^{2}$
Given $V = \frac{V _{ma x}}{2} \Rightarrow \frac{aω}{2}$
$\frac{a ^{2} ω ^{2}}{4} = ω^{2} a^{2} - ω^{2} x^{2}$
$x = \frac{3}{2} a$

Q. A particle executes S.H.M with amplitude ′a′ and time period T. The displacement of the particle when its speed is half of maximum speed is 2x​a​. The value of x is ____________ .

Fora particle executes S.H.M V=ωa2−x2​ Given V=2Vmax​​⇒2aω​ 4a2ω2​=ω2a2−ω2x2 x=23​​a

Q. A particle executes S.H.M with amplitude $^{'} a^{'}$ and time period $T .$ The displacement of the particle when its speed is half of maximum speed is $\frac{x a}{2} .$ The value of $x$ is ____________ .

Fora particle executes S.H.M
$V = ω a^{2} - x^{2}$
Given $V = \frac{V _{ma x}}{2} \Rightarrow \frac{aω}{2}$
$\frac{a ^{2} ω ^{2}}{4} = ω^{2} a^{2} - ω^{2} x^{2}$
$x = \frac{3}{2} a$