Oscillations Test

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Oscillations Test - 12

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Weekly Quiz Competition

Question 1
1 / -0

If a particle is oscillating on the same horizontal plane on the ground.

A
It has only kinetic energy but no potential energy

B
It has only potential energy and no kinetic energy

C
It has both kinetic and potential energy

D
None of these

Solution

A particle oscillating on ground possess both kinetic as well as potential energy.
Question 2
1 / -0

What is the effect on the time period of a simple pendulum if the mass of the bob is doubled?

A
Halved

B
Doubled

C
Becomes $$8$$ times

D
No effect

Solution

As $$T=2 \pi \sqrt{\dfrac{L}{g}}$$
It can be seen that T is independent of mass.
Question 3
1 / -0

The function $$sin ^2(\omega t)$$ represents :

A
A periodic, but not simple harmonic motion with a period $$2\pi /\omega$$

B
A periodic, but not simple harmonic motion with a period $$\pi / \omega$$

C
A simple harmonic motion with a period $$2\pi /\omega$$

D
A simple harmonic motion with a period $$\pi / \omega $$.

Solution
Question 4
1 / -0

The equation of motion of a particle is $$x = a cos(\alpha t)^2$$. The motion is

A
periodic but not oscillatory

B
periodic and oscillatory

C
oscillatory but not periodic

D
neither periodic nor oscillatory.

Solution

The motion is oscillatory but not periodic because the oscillations are followed from the maximum displacement (negative extreme) at t=0, the corresponding echo is equal to π/2
Question 5
1 / -0

Directions For Questions

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The equation of simple harmonic wave is given by $$y=5$$sin $$\dfrac{5}{2}(100 t - x)$$, where $$x$$ and $$y$$ are in meter and time is in second. The time period of the wave (in second) will be.

A
$$0.04$$

B
$$0.06$$

C
$$0.01$$

D
$$0.05$$

Solution

$$y =5$$sin $$\dfrac{\pi}{2}(100 t - x)$$
$$y= A$$sin$$(\omega t - kx)$$
$$\omega = \dfrac{2\pi}{T} $$
$$T=\dfrac{2 \pi}{100}$$
$$\Rightarrow T=0.06$$
Hence, the correct option is $$(B)$$
Question 6
1 / -0

The displacement of a particle from its mean position (in meter) is given by $$Y= 0.2\ sin (10 \pi t+1.5 )\ cos\ (10 \pi t+1.5 )$$.
The motion of the particle is

A
periodic but not $$SHM$$

B
Non - Periodic

C
$$SHM$$ with period $$0.1\ sec$$

D
$$SHM$$ with period $$0.2\ sec$$

Solution
Question 7
1 / -0

Equation of SHM is x = 10 sin 10 $$\pi$$t. Then the time period is, x is in cm and t is in sec

A
10 $$\pi$$

B
0.2 sec

C
0.1 sec

D
2 sec

Solution

Given,
$$x=10\sin(10\pi t)$$

Comparing with $$x=A\sin(\omega t)$$

$$\omega=10\pi$$

$$T=\dfrac{2\pi}{\omega}=\dfrac{2\pi}{10\pi}=0.2$$

Option $$\textbf B$$ is the correct answer
Question 8
1 / -0

Time period will be minimum when d is equal to

A
L/$$\sqrt{12}$$

B
L/$$\sqrt{6}$$

C
L/4

D
L/2
Question 9
1 / -0

When a spring having spring constant $$2Nm^{-1}$$ is stretched by 5 cm, the energy stored in it is:

A
0.025 J

B
0.0025 J

C
0.25 J

D
0.5 J

Solution

Correct answer should be B.
Question 10
1 / -0

For a body in $$S.H.M$$ the velocity is given by the relation $$v=\sqrt{144-16x^2}m/sec$$. The maximum acceleration is

A
$$12 m/sec^2$$

B
$$16 m/sec^2$$

C
$$36 m/sec^2$$

D
$$48 m/sec^2$$

Solution

velocity of the particle in SHM,
$$v=\sqrt{144-16x^{2}}=4\sqrt{9-x^{2}}$$

comparing with $$v=\sqrt{A^{2}-x^{2}}$$
we get $$A=3m$$ $$w=4rad/s$$

so, maximum acceleration,
$$a_{max}=Aw^{2}$$
$$=3\times 4^{2}$$
$$\Rightarrow a_{max}=48m/s^{2}$$

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Re-Attempt Weekly Quiz Competition

Oscillations Test - 12

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Oscillations Test - 12

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SHARING IS CARING

Question 1

It has only kinetic energy but no potential energy

It has only potential energy and no kinetic energy

It has both kinetic and potential energy

None of these

Solution

Question 2

Halved

Doubled

Becomes $$8$$ times

No effect

Solution

Question 3

A periodic, but not simple harmonic motion with a period $$2\pi /\omega$$

A periodic, but not simple harmonic motion with a period $$\pi / \omega$$

A simple harmonic motion with a period $$2\pi /\omega$$

A simple harmonic motion with a period $$\pi / \omega $$.

Solution

Question 4

periodic but not oscillatory

periodic and oscillatory

oscillatory but not periodic

neither periodic nor oscillatory.

Solution

Question 5

$$0.04$$

$$0.06$$

$$0.01$$

$$0.05$$

Solution

Question 6

periodic but not $$SHM$$

Non - Periodic

$$SHM$$ with period $$0.1\ sec$$

$$SHM$$ with period $$0.2\ sec$$

Solution

Question 7

10 $$\pi$$

0.2 sec

0.1 sec

2 sec

Solution

Question 8

L/$$\sqrt{12}$$

L/$$\sqrt{6}$$

L/4

L/2

Question 9

0.025 J

0.0025 J

0.25 J

0.5 J

Solution

Question 10

$$12 m/sec^2$$

$$16 m/sec^2$$

$$36 m/sec^2$$

$$48 m/sec^2$$

Solution

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