Oscillations Test

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Oscillations Test - 34

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Weekly Quiz Competition

Question 1
1 / -0

"A bird flapping its wings circles around a clock tower". Which part of the motion is periodic and oscillatory ?

A
Bird's motion is oscillatory while wing flapping was periodic

B
Both bird's motion and wing flapping were oscillatory

C
Bird's motion is periodic while wing flapping was oscillatory

D
Both bird's motion and wing flapping are non-oscillatory

Solution

Flapping of wings was oscillatory, since it constitutes to and fro motion, while birds motion along a circle is periodic

Thus the correct option is (c)
Question 2
1 / -0

Simple harmonic motion of a particle can be described as the motion of a particle in which

A
smaller oscillations takes place about the mean position

B
acceleration of the particle is proportional to displacement

C
velocity of the particle is proportional to instantaneous displacement

D
displacement of the particle is constant

Solution

Simple harmonic motion is the motion of a particle, in which the acceleration of the particle is proportional to displacement of the particle

The correct option is (b)
Question 3
1 / -0

Which of the following equations represents a particle performing simple harmonic motion

A
x= 3t

B
x = 4 sin 2t

C
x = 1/t

D
x = 3 log 2t

Solution

x = 4 sin 2t is the only periodic function amongst the four options and if this function is differentiated twice, it will give rise to the same function, which clearly says acceleration is proportional to displacement

Thus, option (b) is the correct option
Question 4
1 / -0

A particle performs SHM given by the equation $$x = A sin \omega t$$. Where is the particle at t = 3T/8,

A
The particle is at a distance of $$A/\sqrt(2)$$ moving away from the mean position to its extreme

B
The particle is at a distance of $$A/\sqrt(2)$$ moving towards the mean position to its extreme

C
The particle is at a distance of $$A(1-1/\sqrt(2))$$ moving away from the mean position to its extreme

D
None of these

Solution

From the equation of SHM, it is clear that the particle has started from rest at the mean position.

at t=T/4 =2T/8, the particle would have reached the extreme position
at t = 3T/8, the particle will be returning towards the mean position

Substituting t =3T/8, we get, $$x=A sin [(2 \pi /T)(3T/8)]= A sin (3 \pi/4)=A/\sqrt(2)$$

The displacement of the particle from mean position is $$A/\sqrt(2)$$

The correct answer is (b)
Question 5
1 / -0

For what phase difference between two SHMs will the amplitude of the resultant SHM be zero

A
$$\pi/2$$

B
$$2\pi$$

C
$$\pi$$

D
$$0$$

Solution

Let two SHM equations are $$x_1= Asin(\omega t)$$ and $$x_2= Asin(\omega t+ \delta)$$,
$$\Rightarrow x= x_1+ x_2= Asin(\omega t) +Asin(\omega t+\delta)$$
$$\Rightarrow x= R sin(\omega t+ \phi)$$
$$\Rightarrow R= \sqrt{A^2 +A^2 +2A\times Acos(\delta)}$$
Since $$R=0$$, $$\Rightarrow A^2 + A^2 + 2A^2cos(\delta)=0$$ $$\Rightarrow cos(\delta) = -1$$
$$\therefore \delta = \pi$$, Required phase difference is $$\pi$$
Question 6
1 / -0

In periodic motion, the displacement is

A
directly proportional to the restoring force

B
inversely proportional to the restoring force

C
independent of restoring force

D
independent of any force acting on the particle

Solution

The displacement of the body from its equilibrium is directly proportional to the restoring force. Therefore, higher the displacement, higher is the restoring force.

The correct option is (a)
Question 7
1 / -0

A particle performing SHM has a period of 6s and amplitude of 8 cm. The particle starts from the mean position and moves towards the positive extremity. At what time will it have the maximum amplitude

A
6s

B
4.5s

C
1.5 s

D
3 s

Solution

The time period of SHM is 6 secs. The time taken to reach one extreme is T/4 = 1.5 secs

The correct option is (c)
Question 8
1 / -0

If the phase difference between two sinusoidal waves is $$\pi/2$$, what is the corresponding path difference

A
$$2\lambda/4$$

B
$$\lambda$$

C
$$\lambda/4$$

D
$$\lambda/2$$

Solution

Path difference and phase difference are related by the formula Path difference = $$(\lambda/2 \pi) \times$$ phase difference$$=(\lambda/2 \pi) \times (\pi/2)=\lambda/4$$

The correct option is (c)
Question 9
1 / -0

If two SHMs of different amplitudes are added together, the resultant SHM will be a maximum if the phase difference between them is

A
$$\pi/2$$

B
$$\pi/4$$

C
$$\pi$$

D
$$2\pi$$

Solution

If two SHMs of different amplitudes $$A$$ and $$B$$ are superimposed with each other, then the amplitude of the resultant SHM is given by $$R=\sqrt(A^2+B^2+2AB cos \delta); \delta$$ is the phase difference between the SHMs

The resultant amplitude will be maximum, if the phase difference between them is 0 or $$2\pi$$

The correct option is (d)
Question 10
1 / -0

What is the velocity of the particle executing SHM at x = A/2, if the angular frequency = 2 rads/s and amplitude is 5 cm:

A
$$5 $$cm/s

B
$$0 $$cm/s

C
$$5 \sqrt(3) $$cm/s

D
$$5 \sqrt(2) $$cm/s

Solution

We know that $$v^2=\omega^2(A^2-x^2).$$

Substituting the values of A = 5 cm and $$\omega = 2, x= A/2 $$, we get,

$$v=\omega \sqrt(3) A/2=5 \sqrt(3)$$

The correct option is (c)

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Oscillations Test - 34

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Oscillations Test - 34

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SHARING IS CARING

Question 1

Bird's motion is oscillatory while wing flapping was periodic

Both bird's motion and wing flapping were oscillatory

Bird's motion is periodic while wing flapping was oscillatory

Both bird's motion and wing flapping are non-oscillatory

Solution

Question 2

smaller oscillations takes place about the mean position

acceleration of the particle is proportional to displacement

velocity of the particle is proportional to instantaneous displacement

displacement of the particle is constant

Solution

Question 3

x= 3t

x = 4 sin 2t

x = 1/t

x = 3 log 2t

Solution

Question 4

The particle is at a distance of $$A/\sqrt(2)$$ moving away from the mean position to its extreme

The particle is at a distance of $$A/\sqrt(2)$$ moving towards the mean position to its extreme

The particle is at a distance of $$A(1-1/\sqrt(2))$$ moving away from the mean position to its extreme

None of these

Solution

Question 5

$$\pi/2$$

$$2\pi$$

$$\pi$$

$$0$$

Solution

Question 6

directly proportional to the restoring force

inversely proportional to the restoring force

independent of restoring force

independent of any force acting on the particle

Solution

Question 7

6s

4.5s

1.5 s

3 s

Solution

Question 8

$$2\lambda/4$$

$$\lambda$$

$$\lambda/4$$

$$\lambda/2$$

Solution

Question 9

$$\pi/2$$

$$\pi/4$$

$$\pi$$

$$2\pi$$

Solution

Question 10

$$5 $$cm/s

$$0 $$cm/s

$$5 \sqrt(3) $$cm/s

$$5 \sqrt(2) $$cm/s

Solution

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