Oscillations Test

Result

Oscillations Test - 75

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Weekly Quiz Competition

Question 1
1 / -0

The equation of a damped simple harmonic motion is $$m\frac{d^{2}x}{dt^{2}}+b\frac{dx}{dt}+kx=0$$. Then the angular frequency of oscillation is

A
$$\omega =(\frac{k}{m}-\frac{b^{2}}{4m^{2}})^{1/2}$$

B
$$\omega =(\frac{k}{m}-\frac{b}{4m})^{1/2}$$

C
$$\omega =(\frac{k}{m}-\frac{b^{2}}{4m})^{1/2}$$

D
$$\omega =(\frac{k}{m}-\frac{b^{2}}{4m^{2}})$$

Solution
Question 2
1 / -0

A paramedical staff nurse improvises a second's pendulum (time period 2 s) by fixing one end of a string of length $$L$$ to a ceiling and the other end to a heavy object of negligible size. Within 60 oscillations of this pendulum, she finds that the pulse of a wounded soldier beats 110 times. A symptom of bradycardia is pulse $$< 60$$ per minute and that of tachycardiais $$> 100$$ per minute. Then the length of the string is nearly symptoms of

A
I $$m ,$$ bradycardia

B
$$4 \mathrm { m } ,$$ bradycardia

C
I m, tachycardia

D
$$4 \mathrm { m } ,$$ tachycardia

Solution
Question 3
1 / -0

A bob of a simple pendulum executing SHM in air has time period $$T_o$$ and in water has time period T. Neglect friction. Relation between T and $$T_o$$ if density of bob is $$4/3 \times 10^3 kg/m^3$$, is

A
$$T=T_o$$

B
$$T=\dfrac{T_0}{2}$$

C
$$T=2T_o$$

D
$$T=4T_o$$

Solution
Question 4
1 / -0

Two graphs of the same harmonic wave are shown below. The graph (1) on the left shows the displacement of wave y, as a function of position x for a given instant of time. The graph (2) on the right shows the displacement of a wave as a function of time 't' for a given position. The speed of the wave is

A
5.0 $$cms^{2}$$

B
0.5$$cms^{2}$$

C
0.4$$cms^{2}$$

D
4.0$$cms^{2}$$

Solution
Question 5
1 / -0

A simple pendulum with a bob of mass m swings with angular amplitude of $$60^o$$, when its angular displacement $$30^o$$, find the tension of string

A
$$\dfrac{mg}{2}$$

B
$$\dfrac{3\sqrt{3}mg}{2}$$

C
$$\dfrac{mg}{3}{(3\sqrt{3} - 2)}$$

D
$$\dfrac{\sqrt{3}mg}{2}$$
Question 6
1 / -0

The mass of the bob of a simple pendulum of length L is m. If the bob is left from its horizontal position then the speed of the bob and the tension in the thread at the lowest position of the bob will be respectively :-

A
$$\sqrt{2gL}$$ and 3 mg

B
3 mg and $$\sqrt{2gL}$$

C
2 mg and $$\sqrt{2gL}$$

D
2 gL and 3 mg
Question 7
1 / -0

A simple pendulum is vibrating with an an angolar amplitude of $$90 ^ { \circ }$$,For what values of with vertical, the accelcration is directed
In sertically upwards
2) horizontally
vertically downwerds

A
$$0 ^ { \circ } , \cos ^ { - 1 } \frac { 1 } { \sqrt { 3 } } , 90 ^ { \circ }$$

B
$$\cos ^ { - 4 } \left( \frac { 1 } { \sqrt { 3 } } \right) \cdot \cos w$$

C
$$90 ^ { \circ } , \cos ^ { - 1 } \frac { 1 } { \sqrt { 3 } } , 0 ^ { \circ }$$

D
$$\cos ^ { 4 } \left( \frac { 1 } { \sqrt { 3 } } \right) \cdot \infty , \sigma$$

Solution
Question 8
1 / -0

A simple harmonic motion is given by $$ y= 5 ( sin 3\pi t +\sqrt3 cos 3 \pi t)$$. What is the amplitude of motion if y in m?

A
$$10 $$ cm

B
$$5 $$ cm

C
$$200 $$ cm

D
$$1000 $$ cm

Solution
Question 9
1 / -0

Under the action of a force $$ F = -kx^3$$, the motion of a particle is ($$k$$= a positive constant)

A
simple harmonic motion

B
uniformly accelerated motion

C
not periodic

D
periodic but not simple harmonic

Solution
Question 10
1 / -0

A particle of mass m moving in a one-dimensional potential energy $$U(x) = -ax^{2} + bx^{4}$$, where 'a' and 'b' are positive constants. The angular frequency of small oscillations about the minima of the potential energy is equal to

A
$$2\sqrt { \frac { a }{ 2b } } $$

B
$$2\sqrt { \frac { a }{ m } } $$

C
$$\sqrt { \frac { 2a }{ m } } $$

D
$$\sqrt { \frac { a }{ 2m } } $$

Solution