Oscillations Test

Result

Oscillations Test - 76

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Question 1
1 / -0

Time period of a simple pendulum is $$T$$ and its angular amplitude is $$\theta_{0}$$. Find time taken by the bob to move from equilibrium position $$O$$ to $$P$$ if at this instant string makes an angle $$\theta$$ with the vertical.

A
$$\dfrac{T}{\pi}\sin^{-1}\dfrac{\theta}{\theta_{0}}$$

B
$$\dfrac{T}{2 \pi}\sin^{-1}\dfrac{\theta}{\theta_{0}}$$

C
$$T\sin^{-1}\dfrac{\theta_{0}}{\theta}$$

D
$$T\sin^{-1}\dfrac{\theta}{\theta_{0}}$$
Question 2
1 / -0

A simple pendulum has a bob suspended by an inextensible thread of length $$1$$ metre from a point $$A$$ of suspension. At the extreme position of oscillation, the thread is suddenly caught by a peg at a point $$B$$ distant $$( 1 / 4 )$$ from $$A$$ and the bob begins to oscillate in the new condition. The change in frequency of oscillation of the pendulum is approximately given by $$\left( g=10{ m }/{ s }^{ { 2 } } \right) .$$

A
$$\dfrac { \sqrt { 10 } } { 2 }$$ Hz

B
$$\dfrac { 1 } { 4 \sqrt { 10 } }$$ Hz

C
$$\dfrac { \sqrt { 10 } } { 3 }$$ Hz

D
$$\dfrac { 1 } { \sqrt { 10 } }$$ Hz

Solution
Question 3
1 / -0

A particle executes simple harmonic motion according to equation $$4\dfrac{{{d^2}x}}{{d{t^2}}} + 320 x = 0$$. Its time period of oscillation is

A
$$\dfrac{{2\pi }}{{5\sqrt 3 }}\ s$$

B
$$\dfrac{\pi }{{3\sqrt 2 }}\ s$$

C
$$\dfrac{\pi }{{2\sqrt 5 }}\ s$$

D
$$\dfrac{{2\pi }}{{\sqrt 3 }}\ s$$

Solution
Question 4
1 / -0

The displacement of a body executing S.H.M from its mean portion is given by $$x = 0.5 \sin ( 10 \pi t + 1.5 ) \cos ( 10 \pi t + 1.5 ) $$. The ratio of the maximum velocity to the maximum acceleration of the body is given by

A
$$20 \pi$$

B
$$\frac { 1 } { 20 \pi }$$

C
$$\frac { 1 } { 10 \pi }$$

D
$$10 \pi$$

Solution
Question 5
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If $$\vec { F } $$ force vector, $$\vec { v } $$ is velocity vector, $$\vec { a }$$ vector is acceleration vector and $$\vec { r}$$ vector is displacement vector with respect to mean position than which of the following quantities are always non-negative in a simple harmonic motion along a straight line?

A
$$\vec { F } .\vec { a} $$

B
$$\vec { V } .\vec { r} $$

C
$$\vec { a } .\vec { r} $$

D
$$\vec { F } .\vec { r} $$

Solution
Question 6
1 / -0

A simple pendulum of period T has a metal bob which is negatively charged. If it is allowed to oscillate above a positively charged metal plate its period will be

A
Remains equal to T

B
Less than T

C
Greater than T

D
Infinite

Solution
Question 7
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Two identical springs are fixed at one end and masses 1$$\mathrm { kg }$$ and 4$$\mathrm { kg }$$ are suspended at their other ends. Theyare both stretched down from their mean position and let go simultaneously. If they are in the same phase atter every 4 seconds then the springs constant $$\mathrm { k }$$ is

A
$$\pi \frac { N } { m }$$

B
$$\pi ^ { 2 } \frac { \mathrm { N } } { \mathrm { m } }$$

C
2$$\pi \frac { \mathrm { N } } { \mathrm { m } }$$

D
given data is insufficient

Solution
Question 8
1 / -0

In simple harmonic motion, the graph between kinetic energy K and time 't' is :

A

B

C
none

D
both

Solution
Question 9
1 / -0

The potential energy of a simple harmonic oscillator of mass 2 kg in its mean position is 5J If its total energy is 9J and Its amplitude is 0.01 its time period would be

A
$$\frac { \pi } { 10 } \mathrm { sec }$$

B
$$\frac { \pi } { 20 } \mathrm { sec }$$

C
$$\frac { \pi } { 50 } \mathrm { sec }$$

D
$$\frac { \pi } { 100 } \mathrm { sec }$$

Solution
Question 10
1 / -0

A particle is performing SHM with energy of vibration $$90$$ $$ \mathrm{J} $$ and amplitude 6 $$ \mathrm{cm} $$ . When the particlere aches at distance 4 $$ \mathrm{cm} $$ from mean position, it is stopped for a moment and then released. The new energy of vibration will be

A
40 $$ \mathrm{J} $$

B
50 $$ \mathrm{J} $$

C
90 $$ \mathrm{J} $$

D
60 $$ \mathrm{J} $$

Solution