1
AIEEE 2012
+4
-1
Out of Syllabus
If a simple pendulum has significant amplitude (up to a factor of $$1/e$$ of original ) only in the period between $$t = 0s\,\,to\,\,t = \tau \,s,$$ then $$\tau \,$$ may be called the average life of the pendulum When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity with $$b$$ as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds :
A
$${{0.693} \over b}$$
B
$$b$$
C
$${1 \over b}$$
D
$${2 \over b}$$
2
AIEEE 2011
+4
-1
A mass $$M,$$ attached to a horizontal spring, executes $$S.H.M.$$ with amplitude $${A_1}.$$ When the mass $$M$$ passes through its mean position then a smaller mass $$m$$ is placed over it and both of them move together with amplitude $${A_2}.$$ The ratio of $$\left( {{{{A_1}} \over {{A_2}}}} \right)$$ is :
A
$${{M + m} \over M}$$
B
$${\left( {{M \over {M + m}}} \right)^{{1 \over 2}}}$$
C
$${\left( {{{M + m} \over M}} \right)^{{1 \over 2}}}$$
D
$${M \over {M + m}}$$
3
AIEEE 2011
+4
-1
Two particles are executing simple harmonic motion of the same amplitude $$A$$ and frequency $$\omega$$ along the $$x$$-axis. Their mean position is separated by distance $${X_0}\left( {{X_0} > A} \right)$$. If the maximum separation between them is $$\left( {{X_0} + A} \right),$$ the phase difference between their motion is:
A
$${\pi \over 3}$$
B
$${\pi \over 4}$$
C
$${\pi \over 6}$$
D
$${\pi \over 2}$$
4
AIEEE 2009
+4
-1
If $$x,$$ $$v$$ and $$a$$ denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period $$T,$$ then, which of the following does not change with time?
A
$$aT/x$$
B
$$aT + 2\pi v$$
C
$$aT/v$$
D
$${a^2}{T^2} + 4{\pi ^2}{v^2}$$
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