Question

The mass $$M$$ shown in the figure oscillates in simple harmonic motion with amplitude $$A.$$ The amplitude of the point $$P$$ is
Simple Harmonic Motion (SHM) mcq question image

A. $$\frac{{{k_1}A}}{{{k_2}}}$$
B. $$\frac{{{k_2}A}}{{{k_1}}}$$
C. $$\frac{{{k_1}A}}{{{k_1} + {k_2}}}$$
D. $$\frac{{{k_2}A}}{{{k_1} + {k_2}}}$$  
Answer :   $$\frac{{{k_2}A}}{{{k_1} + {k_2}}}$$
Solution :
Simple Harmonic Motion (SHM) mcq solution image
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
$$\eqalign{ & {x_1} + {x_2} = A\,......\,\left( {\text{i}} \right) \cr & {\text{and }}{k_1}{x_1} = {k_2}{x_2} \Rightarrow {x_2} = \frac{{{k_1}{x_1}}}{{{k_2}}}\,......\,\left( {{\text{ii}}} \right) \cr & {\text{From}}\left( {\text{i}} \right)\& \left( {{\text{ii}}} \right) \cr & {x_1} + \frac{{{k_1}{x_1}}}{{{k_2}}} = A \Rightarrow {x_1} = \frac{{{k_2}A}}{{{k_2} + {k_1}}} \cr} $$

Releted MCQ Question on
Oscillation and Mechanical Waves >> Simple Harmonic Motion (SHM)

Releted Question 1

Two bodies $$M$$ and $$N$$ of equal masses are suspended from two separate massless springs of spring constants $${k_1}$$ and $${k_2}$$ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of vibration of $$M$$ to that of $$N$$ is

A. $$\frac{{{k_1}}}{{{k_2}}}$$
B. $$\sqrt {\frac{{{k_1}}}{{{k_2}}}} $$
C. $$\frac{{{k_2}}}{{{k_1}}}$$
D. $$\sqrt {\frac{{{k_2}}}{{{k_1}}}} $$
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Releted Question 2

A particle free to move along the $$x$$-axis has potential energy given by $$U\left( x \right) = k\left[ {1 - \exp \left( { - {x^2}} \right)} \right]$$      for $$ - \infty \leqslant x \leqslant + \infty ,$$    where $$k$$ is a positive constant of appropriate dimensions. Then

A. at points away from the origin, the particle is in unstable equilibrium
B. for any finite nonzero value of $$x,$$ there is a force directed away from the origin
C. if its total mechanical energy is $$\frac{k}{2},$$  it has its minimum kinetic energy at the origin.
D. for small displacements from $$x = 0,$$  the motion is simple harmonic
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Releted Question 3

The period of oscillation of a simple pendulum of length $$L$$ suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination $$\alpha ,$$ is given by

A. $$2\pi \sqrt {\frac{L}{{g\cos \alpha }}} $$
B. $$2\pi \sqrt {\frac{L}{{g\sin \alpha }}} $$
C. $$2\pi \sqrt {\frac{L}{g}} $$
D. $$2\pi \sqrt {\frac{L}{{g\tan \alpha }}} $$
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Releted Question 4

A particle executes simple harmonic motion between $$x = - A$$  and $$x = + A.$$  The time taken for it to go from 0 to $$\frac{A}{2}$$ is $${T_1}$$ and to go from $$\frac{A}{2}$$ to $$A$$ is $${T_2.}$$ Then

A. $${T_1} < {T_2}$$
B. $${T_1} > {T_2}$$
C. $${T_1} = {T_2}$$
D. $${T_1} = 2{T_2}$$
View Answer

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Simple Harmonic Motion (SHM)

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