The mass \[M\]shown in the figure oscillates in simple harmonic motion with amplitude \[A\]. The amplitude of the point \[P\] is |
A) \[\frac{{{k}_{1}}A}{{{k}_{2}}}\]
B) \[\frac{{{k}_{2}}A}{{{k}_{1}}}\]
C) \[\frac{{{k}_{1}}A}{{{k}_{1}}+{{k}_{2}}}\]
D) \[\frac{{{k}_{2}}A}{{{k}_{1}}+{{k}_{2}}}\]
Correct Answer: D
Solution :
In case (ii), the springs are shown in the maximum compressed position. If the spring of spring constant \[{{k}_{1}}\] is compressed by \[{{x}_{1}}\] and that of spring constant \[{{k}_{2}}\] is compressed by \[{{x}_{2}}\] then | |||
\[{{x}_{1}}+{{x}_{2}}=A\] | ? (i) | ||
\[{{k}_{1}}{{x}_{1}}={{k}_{2}}{{x}_{2}}\Rightarrow {{x}_{2}}=\frac{{{k}_{1}}{{x}_{1}}}{{{k}_{2}}}\] | ? (ii) | ||
From (i) and (ii) | |||
\[{{x}_{1}}+\frac{{{k}_{1}}{{x}_{1}}}{{{k}_{2}}}=A\Rightarrow {{x}_{1}}=\frac{{{k}_{2}}A}{{{k}_{2}}+{{k}_{1}}}\] | |||
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