1
AIEEE 2007
MCQ (Single Correct Answer)
+4
-1
A particle of mass $$m$$ executes simple harmonic motion with amplitude a and frequency $$v.$$ The average kinetic energy during its motion from the position of equilibrium to the end is
A
$$2{\pi ^2}\,m{a^2}{v^2}$$
B
$${\pi ^2}\,m{a^2}{v^2}$$
C
$${1 \over 4}\,m{a^2}{v^2}$$
D
$$4{\pi ^2}m{a^2}{v^2}$$
2
AIEEE 2007
MCQ (Single Correct Answer)
+4
-1
A point mass oscillates along the $$x$$-axis according to the law $$x = {x_0}\,\cos \left( {\omega t - \pi /4} \right).$$ If the acceleration of the particle is written as $$a = A\,\cos \left( {\omega t + \delta } \right),$$ then
A
$$A = {x_0}{\omega ^2},\,\,\delta = 3\pi /4$$
B
$$A = {x_0},\,\,\delta = - \pi /4$$
C
$$A = {x_0}{\omega ^2},\,\,\delta = \pi /4$$
D
$$A = {x_0}{\omega ^2},\,\,\delta = - \pi /4$$
3
AIEEE 2007
MCQ (Single Correct Answer)
+4
-1
The displacement of an object attached to a spring and executing simple harmonic motion is given by $$x = 2 \times {10^{ - 2}}$$ $$cos$$ $$\pi t$$ metre. The time at which the maximum speed first occurs is
A
$$0.25$$ $$s$$
B
$$0.5$$ $$s$$
C
$$0.75$$ $$s$$
D
$$0.125$$ $$s$$
4
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
A coin is placed on a horizontal platform which undergoes vertical simple harmonic motoin of angular frequency $$\omega .$$ The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time
A
at the mean position of the platform
B
for an amplitude of $${g \over {{\omega ^2}}}$$
C
For an amplitude of $${{{g^2}} \over {{\omega ^2}}}$$
D
at the height position of the platform
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