1
AIEEE 2004
+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
$${m \over {\omega _0^2 + {\omega ^2}}}$$
2
AIEEE 2004
+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
$${\omega _1} < {\omega _2}$$
3
AIEEE 2003
+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
$${5 \over 3}$$
4
AIEEE 2003
+4
-1
Two particles $$A$$ and $$B$$ of equal masses are suspended from two massless springs of spring of spring constant $${k_1}$$ and $${k_2}$$, respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of $$A$$ and $$B$$ is
A
$$\sqrt {{{{k_1}} \over {{k_2}}}}$$
B
$${{{{k_2}} \over {{k_1}}}}$$
C
$$\sqrt {{{{k_2}} \over {{k_1}}}}$$
D
$${{{{k_1}} \over {{k_2}}}}$$
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