If the displacement (x) and velocity (v) of a particle executing SHM are related through the expression 3 v2=30-x2, then its time period is s. (Take √3=1.73 )

Question

If the displacement (x) and velocity (v) of a particle executing SHM are related through the expression 3 v2=30-x2, then its time period is s. (Take √3=1.73 ) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Given equation, 3 v2=30-x2 Differentiating both sides, we get 6 v (d v/d x)=-2 x ⇒ v (d v/d x)=(-1/3) x ⇒ (a/x)=(-1/3) ldots[∵ a=(d v/d t)=(d v/d x) (d x/d t)=v (d v/d x)] T =(2 π/√ mid ( text acceleration ) text displacement )=(2 π/|(-1)3|)=2 π √3 ∴ T =10.86 sec

Q. If the displacement (x) and velocity (v) of a particle executing SHM are related through the expression 3v2=30−x2, then its time period is _____s. (Take 3​=1.73 )

Given equation, 3v2=30−x2 Differentiating both sides, we get 6vdxdv​=−2x ⇒vdxdv​=3−1​x ⇒xa​=3−1​ …[∵a=dtdv​=dxdv​dtdx​=vdxdv​] T=∣ displacement acceleration ​​2π​=∣3−1​∣2π​=2π3​ ∴T=10.86sec

Q. If the displacement $(x)$ and velocity $(v)$ of a particle executing SHM are related through the expression $3 v^{2} = 30 - x^{2}$ , then its time period is _____ $s$ . (Take $3 = 1.73$ )