1
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
A particle at the end of a spring executes $$S.H.M$$ with a period $${t_1}$$. While the corresponding period for another spring is $${t_2}$$. If the period of oscillation with the two springs in series is $$T$$ then
A
$${T^{ - 1}} = t_1^{ - 1} + t_2^{ - 1}$$
B
$${T^2} = t_1^2 + t_2^2$$
C
$$T = {t_1} + {t_2}$$
D
$${T^{ - 2}} = t_1^{ - 2} + t_2^{ - 2}$$
2
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
A particle of mass $$m$$ is attached to a spring (of spring constant $$k$$) and has a natural angular frequency $${\omega _0}.$$ An external force $$F(t)$$ proportional to $$\cos \,\omega t\left( {\omega \ne {\omega _0}} \right)$$ is applied to the oscillator. The time displacement of the oscillator will be proportional to
A
$${1 \over {m\left( {\omega _0^2 + {\omega ^2}} \right)}}$$
B
$${1 \over {m\left( {\omega _0^2 - {\omega ^2}} \right)}}$$
C
$${m \over {\omega _0^2 - {\omega ^2}}}$$
D
$${m \over {\omega _0^2 + {\omega ^2}}}$$
3
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
In forced oscillation of a particle the amplitude is maximum for a frequency $${\omega _1}$$ of the force while the energy is maximum for a frequency $${\omega _2}$$ of the force; then
A
$${\omega _1} < {\omega _2}$$ when damping is small and $${\omega _1} > {\omega _2}$$ when damping is large
B
$${\omega _1} > {\omega _2}$$
C
$${\omega _1} = {\omega _2}$$
D
$${\omega _1} < {\omega _2}$$
4
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
A mass $$M$$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes $$SHM$$ of time period $$T.$$ If the mass is increased by $$m.$$ the time period becomes $${{5T} \over 3}$$. Then the ratio of $${{m} \over M}$$ is
A
$${3 \over 5}$$
B
$${25 \over 9}$$
C
$${16 \over 9}$$
D
$${5 \over 3}$$
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