1
AIEEE 2004
+4
-1
The total energy of particle, executing simple harmonic motion is
A
independent of $$x$$
B
$$\propto \,{x^2}$$
C
$$\propto \,x$$
D
$$\propto \,{x^{1/2}}$$
2
AIEEE 2004
+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
$${T^{ - 2}} = t_1^{ - 2} + t_2^{ - 2}$$
3
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
$${m \over {\omega _0^2 + {\omega ^2}}}$$
4
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
$${\omega _1} < {\omega _2}$$
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