1
AIEEE 2005
+4
-1
If a simple harmonic motion is represented by $${{{d^2}x} \over {d{t^2}}} + \alpha x = 0.$$ its time period is
A
$${{2\pi } \over {\sqrt \alpha }}$$
B
$${{2\pi } \over \alpha }$$
C
$$2\pi \sqrt \alpha$$
D
$$2\pi \alpha$$
2
AIEEE 2004
+4
-1
The bob of a simple pendulum executes simple harmonic motion in water with a period $$t,$$ while the period of oscillation of the bob is $${t_0}$$ in air. Neglecting frictional force of water and given that the density of the bob is $$\left( {4/3} \right) \times 1000\,\,kg/{m^3}.$$ What relationship between $$t$$ and $${t_0}$$ is true
A
$$t = 2{t_0}$$
B
$$t = {t_0}/2$$
C
$$t = {t_0}$$
D
$$t = 4{t_0}$$
3
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
$$\propto \,{x^{1/2}}$$
4
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
$${T^{ - 2}} = t_1^{ - 2} + t_2^{ - 2}$$
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