1
IIT-JEE 2011 Paper 2 Offline
+3
-0.75
A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, $${x_1}\left( t \right) = A\sin \omega t$$ and $${x_2}\left( t \right) = A\sin \left( {\omega t + {{2\pi } \over 3}} \right)$$. Adding a third sinusoidal displacement $${x_3}\left( t \right) = B\sin \left( {\omega t + \phi } \right)$$ brings the mass to a complete rest. The values of B and $$\phi$$ are
A
$$\sqrt 2 A,{{3\pi } \over 4}$$
B
$$A,{{4\pi } \over 3}$$
C
$$\sqrt 3 A,{{5\pi } \over 6}$$
D
$$A,{\pi \over 3}$$
2
IIT-JEE 2011 Paper 2 Offline
+2
-0.5
A wooden block performs $$SHM$$ on a frictionless surface with frequency, $${v_0}.$$ The block carries a charge $$+Q$$ on its surface . If now a uniform electric field $$\overrightarrow E$$ is switched- on as shown, then the $$SHM$$ of the block will be
A
of the same frequency and with shifted mean position.
B
of the same frequency and with the same mean position
C
of changed frequency and with shifted mean position.
D
of changed frequency and with the same mean position.
3
IIT-JEE 2010 Paper 1 Offline
+3
-1

When a particle of mass m moves on the x-axis in a potential of the form V(x) = kx2, it performs simple harmonic motion. The corresponding time period is proportional to $$\sqrt {{m \over k}}$$, as can be seen easily using dimensional analysis. However, the motion of a particle can be periodic even when its potential energy increases on both sides of x = 0 in a way different from kx2 and its total energy is such that the particle does not escape to infinity. Consider a particle of mass m moving on the x-axis. Its potential energy is V(x) = $$\alpha$$x4 ($$\alpha$$ > 0) for | x | near the origin and becomes a constant equal to V0 for (see figure).

If the total energy of the particle is E, it will perform periodic motion only if

A
E < 0
B
E > 0
C
V0 > E > 0
D
E > V0
4
IIT-JEE 2010 Paper 1 Offline
+3
-1

When a particle of mass m moves on the x-axis in a potential of the form V(x) = kx2, it performs simple harmonic motion. The corresponding time period is proportional to $$\sqrt {{m \over k}}$$, as can be seen easily using dimensional analysis. However, the motion of a particle can be periodic even when its potential energy increases on both sides of x = 0 in a way different from kx2 and its total energy is such that the particle does not escape to infinity. Consider a particle of mass m moving on the x-axis. Its potential energy is V(x) = $$\alpha$$x4 ($$\alpha$$ > 0) for | x | near the origin and becomes a constant equal to V0 for (see figure).

For periodic motion of small amplitude A, the time period T of this particle is proportional to

A
$$A\sqrt {m/\alpha }$$
B
$${1 \over A}\sqrt {m/\alpha }$$
C
$$A\sqrt {\alpha /m}$$
D
$${1 \over A}\sqrt {\alpha /m}$$
EXAM MAP
Medical
NEET