Question

Q. Find the value of the displacement of a particle in S.H.M. when its
velocity is half of the maximum velocity.​

Answer 1

Answer:

$x\sqrt{5} \div 2$

Explanation:

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Answer 2

Answer:

The displacement is √3/2x₀

To Find:

Find the value of the displacement of a particle in S.H.M. when its

velocity is half of the maximum velocity.​

Simple Harmonic Motion:

Simple harmonic motion is defined as a periodic motion of a point along a straight line, such that its acceleration is always towards a fixed point in that line and is proportional to its distance from that point

Relation between maximum velocity and instant velocity:

v = v₀{√(1-(x/x₀)²}

v= instant velocity

v₀=maximum velocity

x=instant displacement

x₀=maximum displacement

v =v₀/2

v₀/2 = v₀{√(1-(x/x₀)²}

1/2 = {√(1-(x/x₀)²}

1/4 = 1-(x/x₀)²

(x/x₀)² = 1-1/4

(x/x₀)² = 3/4

x/x₀=√3/2

x= x₀√3/2

Hence the displacement is √3/2x₀