Oscillations Test

Result

Oscillations Test - 49

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Weekly Quiz Competition

Question 1
1 / -0

The amplitude $$(A)$$ of damped oscillator becomes half in $$5$$ minutes. The amplitude after next $$10$$ minutes will be:

A
$$A$$

B
$$\cfrac{A}{8}$$

C
$$\cfrac{A}{4}$$

D
$$4A$$

Solution
Question 2
1 / -0

If velocity of a particle in SHM at x=4 m and x=5 m are 15 m/s and 13 m/s then its time period will be:

A
$$ \pi $$ /4

B
$$ \pi $$ /2

C
$$ \pi $$

D
4$$ \pi $$ /5

Solution
Question 3
1 / -0

The time period of mass suspended from a spring is T. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be:

A
$$\cfrac T 4$$

B
$$T$$

C
$$\cfrac T 2$$

D
$$2 T $$

Solution
Question 4
1 / -0

Select proper wave equation which describes simple harmonic progressive wave travelling along positive $$X$$ axis.

A
$$y = A \sin ( \alpha t + k x )$$

B
$$y = A \cos ( o t + k x )$$

C
$$y = A \sin ( a t - k x )$$

D
$$y = - 4 \tan ( \alpha x - k x )$$

Solution
Question 5
1 / -0

At time t = 0, one particle is at maximum positive amplitude and the other particle is at $$\cfrac{1}{\sqrt{2}}$$ of the positive amplitude. Their amplitudes and time periods T are same. If they are approaching, find the time by which they cross each other :-

A
$$\cfrac {T}{6}$$

B
$$\cfrac {T}{12}$$

C
$$\cfrac {T}{16}$$

D
$$\cfrac {T}{24}$$

Solution
Question 6
1 / -0

A body attached to the lower end of a vertical spring oscillates with time period of 1 sec. The time period when two such springs are connected one below another is approximately:

A
0.7 sec

B
1 sec

C
1.4 sec

D
2 sec

Solution
Question 7
1 / -0

In the arrangement , spring constant K has value $$2N\quad { m }^{ -1 }$$ ,mass M=3kg and mass m= 1kg. Mass M is in contact with a smooth surface . The coefficient of friction between two blocks is 0.1. The time period of SHM executed by the system is :
(assume both move together)

A
$$\pi \sqrt { 6 } $$

B
$$\pi \sqrt { 2 } $$

C
$$2\sqrt { 2}\pi $$

D
$$2\pi $$

Solution
Question 8
1 / -0

A simple harmonic wave is represented by the relation $$y\left ( x,t \right )=a_{0}sin2\pi \left ( vt-\dfrac{x}{\lambda } \right )$$ if the maximum particle velocity is three times the wave velocity, te wavelength $$\lambda $$ of the wave is-

A
$$\pi a_{0}/3$$

B
$$2\pi a_{0}/3$$

C
$$\pi a_{0}$$

D
$$\pi a_{0}/2$$

Solution

$$\begin{array}{l} { V_{ p } }={ a_{ 0 } }\left( { 2\pi V } \right) \\ =2\pi { a_{ 0 } }V \\ { V_{ w } }=\dfrac { { 2\pi V\lambda } }{ { 2\pi } } =V\lambda \\ \Rightarrow 2\pi { a_{ 0 } }=3V\lambda \\ \lambda =\dfrac { 2 }{ 3 } \pi { a_{ 0 } } \\ Hence, \\ option\, \, B\, \, is\, \, correct\, \, answer. \end{array}$$
Question 9
1 / -0

Two bodies A and B of equal mass are suspended from separate massless springs of spring constant $$k_1$$ and $$k_2$$ respectively. If the bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of A to that of B is

A
$$k_1/k_2$$

B
$$\sqrt{k_1/k_2}$$

C
$$k_2/k_1$$

D
$$\sqrt{k_2/k_1}$$

Solution
Question 10
1 / -0

An object undergoing SHM taken 0.5 s to travel from one point of zero velocity to the next such point. The distance between those point is 50 cm. The period, frequency and amplitude of the motion is:

A
$$1s, 1Hz,25 cm$$

B
$$2s.1Hz,50 cm$$

C
$$1s, 2Hz,25 cm$$

D
$$2s, 2Hz,50 cm$$

Solution