Oscillations Test

Result

Oscillations Test - 54

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Question 1
1 / -0

If a particle is acted by two simple harmonic motions simultaneously, the path of particle is:

A
Stream line motion

B
Lissajous figure

C
Just like motion of a particle under gravity

D
None of the above

Solution
Question 2
1 / -0

For a simple pendulum, the graph between $$T^2$$ and $$L$$ is:

A
Straight line passing thorugh origin

B
Parabolic

C
Circle

D
None of the above

Solution
Question 3
1 / -0

The equations of two linear S.H.M.'s are
$$x=a\sin \omega t$$ along x-axis
$$y=a\sin 2\omega t$$ along y-axis
If they act on a particle simultaneously, the trajectory of the particle is:

A
$$\dfrac{y^2}{a^2}+\dfrac{x^2}{4a^2}=1$$

B
$$y^2=\dfrac{4x^2}{a^2}(a^2-x^2)$$

C
$$y^2=2ax$$

D
None of these

Solution
Question 4
1 / -0

A body with speed '$$v$$' is moving along a straight line. At the same time it is at distance $$x$$ from a fixed point on the line, the speed is given by $$v^2=144-9x^2$$. Then:

A
Displacement of the body $$<$$ distance moved by body

B
The magnitude of acceleration at a distance $$3$$m from the fixed point is $$27 m/s^2$$

C
The motion is S.H.M. with $$T=\dfrac{2\pi}{3}$$ unit

D
The maximum displacement from the fixed point is $$4$$ unit

E
All the above

Solution
Question 5
1 / -0

A point mass $$m=20kg$$, is suspended by a massless spring of constant $$2000 N/m$$. The point mass is released when elongation in the spring is $$15cm$$. The equation of displacement of particle as function of time is: (Take $$g=10 m/s^2$$)

A
$$y=10\sin 10t$$

B
$$y=10\cos 10t$$

C
$$y=10\sin\left(10t+\dfrac{\pi}{6}\right)$$

D
None of these

Solution
Question 6
1 / -0

A naughty boy is sitting on the roof of a flat toy car of mass $$6$$ kg. If no slipping takes place between car and the boy then what should be the mass of the child in order to have period of system equal to $$0.758$$ sec?

A
$$2.74$$ kg

B
$$6$$ kg

C
$$3$$ kg

D
None of these

Solution
Question 7
1 / -0

A spring of spring constant $$200N/m$$ has a block of mass $$1 kg$$ hanging at its one end and of other end spring is attached to a ceiling of an elevator. The elevator rising upwards with an acceleration of $$g/3$$. When acceleration is suddenly cease, then what should be the angular frequency and elongation during the time when the elevator is accelerating?

A
$$14.14\ rad/s, \, 0.07m$$

B
$$13\ rad/s, \, 0.1m$$

C
$$14\ rad/s, \, 0.05m$$

D
$$10\ rad/s, \, 0.07m$$

Solution
Question 8
1 / -0

There are two pendulums of length $$l_1$$ and $$l_2$$ which start vibrating. At some instant, the both pendulum are in mean position in the same phase. After how many vibrations of shorter pendulum, the both pendulum will be in phase in the mean position?
$$[(l_1 > l_2), l_1=121 cm, l_2=100 cm]$$

A
$$11$$

B
$$10$$

C
$$9$$

D
$$8$$

Solution
Question 9
1 / -0

A particle of mass m is allowed to oscillate near the minimum of a vertical parabolic path having the equation $$x^2=4ay$$. The angular frequency of small oscillations is given by:

A
$$\sqrt{gh}$$

B
$$\sqrt{2gh}$$

C
$$\sqrt{\left(\dfrac{g}{2a}\right)}$$

D
$$\sqrt{\left(\dfrac{g}{a}\right)}$$

Solution
Question 10
1 / -0

Figure represents two simple harmonic motions.
The parameter which has different value in the two motions is

A
amplitude

B
frequency

C
phase

D
maximum velocity

Solution