1
JEE Main 2014 (Offline)
+4
-1
A particle moves with simple harmonic motion in a straight line. In first $$\tau s,$$ after starting from rest it travels a distance $$a,$$ and in next $$\tau s$$ it travels $$2a,$$ in same direction, then:
A
amplitude of motion is $$3a$$
B
time period of oscillations is $$8\tau$$
C
amplitude of motion is $$4a$$
D
time period of oscillations is $$6\tau$$
2
JEE Main 2013 (Offline)
+4
-1
Out of Syllabus
The amplitude of a damped oscillator decreases to $$0.9$$ times its original magnitude in $$5s$$. In another $$10s$$ it will decrease to $$\alpha$$ times its original magnitude, where $$\alpha$$ equals
A
$$0.7$$
B
$$0.81$$
C
$$0.729$$
D
$$0.6$$
3
JEE Main 2013 (Offline)
+4
-1
An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $$M.$$ The piston and the cylinder have equal cross sectional area $$A$$. When the piston is in equilibrium, the volume of the gas is $${V_0}$$ and its pressure is $${P_0}.$$ The piston is slightly displaced from the equilibrium position and released,. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frquency
A
$${1 \over {2\pi }}\,{{A\gamma {P_0}} \over {{V_0}M}}$$
B
$${1 \over {2\pi }}\,{{{V_0}M{P_0}} \over {{A^2}\gamma }}$$
C
$${1 \over {2\pi }}\,\sqrt {{{A\gamma {P_0}} \over {{V_0}M}}}$$
D
$${1 \over {2\pi }}\,\sqrt {{{M{V_0}} \over {A\gamma {P_0}}}}$$
4
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
$${2 \over b}$$
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