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Forced Oscillations

The mass M sh...

Question

The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. The amplitude of the point P is?

\frac{k_{1} A}{k_{2}}

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\frac{k_{2} A}{k_{1}}

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\frac{k_{1} A}{k_{1} + k_{2}}

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\frac{k_{2} A}{k_{1} + k_{2}}

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Solution

The correct option is D $\frac{k_{2} A}{k_{1} + k_{2}}$
Let force of $F$ be applied
$∴ F = k_{1} x_{1}$
$⟹ x_{1} = \frac{F}{k_{1}}$
also, $F = k_{2} x_{2}$
$⟹ x_{2} = \frac{F}{k_{2}}$
$∴$ Amplitude, $(A) = x_{1} + x_{2} = F (\frac{1}{K_{1}} + \frac{1}{K_{2}})$
$∴ F = \frac{k_{1} k_{2}}{k_{1} + k_{2}} A$
So, the amplitude of $P = \frac{F}{k_{1}} = \frac{k_{2}}{k_{1} + k_{2}} A$

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The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. The amplitude of the point P is?

The correct option is D k2Ak1+k2Let force of F be applied∴F=k1x1⟹x1=Fk1also, F=k2x2⟹x2=Fk2∴ Amplitude, (A)=x1+x2=F(1K1+1K2)∴F=k1k2k1+k2ASo, the amplitude of P=Fk1=k2k1+k2A