A body executing linear simple harmonic motion has a velocity of $3 c m / s$ , when its displacement is $4 c m$ and a velocity of $4 c m / s$ , when its displacement is $3 c m$ . What is the amplitude of oscillation?

5 c m

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7.5 c m

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10 c m

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12.5 c m

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Solution

The correct option is A $5 c m$
In SHM, the velocity $V$ at a displacement $x$ is given by
$V = ω {(A^{2} - x^{2})}^{\frac{1}{2}} o r V^{2} = ω^{2} (A^{2} - x^{2})$
Now
$V = 3 c m / s$
When,
$x = 4 c m . ∴ 9 = ω^{2} (A^{2} - 16) . . . . . . (i)$

Also
$V = 4 c m / s$
When,
$x = 3 c m ∴ 16 = ω^{2} (A^{2} - 9) . . . . . . (i i)$
Simultaneous solution of equations $(i)$ and $(i i)$ gives
$A = 5 c m$

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A body executing linear simple harmonic motion has a velocity of 3 cm/s, when its displacement is 4 cm and a velocity of 4 cm/s, when its displacement is 3 cm. What is the amplitude of oscillation?

The correct option is A 5 cmIn SHM, the velocity V at a displacement x is given by V=ω(A2−x2)12or V2=ω2(A2−x2) Now V=3 cm/s When, x=4 cm.∴9=ω2(A2−16)......(i) Also V=4cm/s When, x=3 cm∴16=ω2(A2−9)......(ii) Simultaneous solution of equations (i) and (ii) gives A=5 cm

A body executing linear simple harmonic motion has a velocity of $3 c m / s$ , when its displacement is $4 c m$ and a velocity of $4 c m / s$ , when its displacement is $3 c m$ . What is the amplitude of oscillation?