Tag: example of simple harmonic motion

Questions Related to example of simple harmonic motion

A simple pendulum is released when $\theta = \pi/6$. The time period of oscillation is

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. $\displaystyle 2\pi\sqrt{\frac{l}{g}}$

  2. $\displaystyle 2\pi\sqrt{\frac{l}{g}}\left(\frac{293}{288}\right)$

  3. $\displaystyle 2\pi\sqrt{\frac{l}{g}}\left(\frac{288}{293}\right)$

  4. none of these

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Correct Option: B
Explanation:

For large amplitudes, the time period is given by 
$T={2\pi }{\sqrt{\dfrac{L}{g}}}(1+\dfrac{\theta ^{2}}{16})$
Substitute $\theta =\dfrac{\pi }{6}$, we get answer as 
$T={2\pi }{\sqrt{\dfrac{L}{g}}}(\dfrac{293}{288})$
Option B is correct.

A pendulum suspended from the ceiling of an elevator at rest has time period ${ T } _{ 1 }$. When the elevator moves up with an acceleration 'a' its time period of oscillation becomes ${ T } _{ 2 }$ when the elevator moves down with an acceleration 'a', its period of oscillation become ${ T } _{ 3 }$ then

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. ${ T } _{ 1 }=\sqrt { { T } _{ 2 }{ T } _{ 3 } } $

  2. ${ T } _{ 1 }=\sqrt { T _{ 2 }{ ^{ 2 }T _{ 3 } }^{ 2 } } $

  3. ${ T } _{ 1 }=\dfrac { \sqrt { 2 } { T } _{ 2 }{ T } _{ 3 } }{ \sqrt { {T _{ 2 }}^{ 2 }+{T _{ 3 } }^{ 2 } } } $

  4. ${ T } _{ 1 }=\dfrac { { T } _{ 2 }{ T } _{ 3 } }{ \sqrt { {T _{ 2 }}^{ 2 }+{T _{ 3 } }^{ 2 } } } $

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Correct Option: D

The centripetal acceleration of the bob of a conical pendulem is......................

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. $\dfrac{mg}{cos \theta}$

  2. $\dfrac{rg}{L}$

  3. $\dfrac{g}{L}$

  4. $\dfrac{g}{L cos \theta}$

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Correct Option: A

The time period of a torsional pendulum is

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. $T=\pi\sqrt{C/I}$

  2. $T=2\pi\sqrt{I/C}$

  3. $T=2\pi\sqrt{C/I}$

  4. $T=\pi\sqrt{I/C}$

Show answer
Correct Option: B
Explanation:

In torsional pendulum, $\omega =\sqrt{\frac{C}{I}}$
$T=\frac{2\pi }{\omega }=2\pi \sqrt{\frac{I}{C}}$
Option B is correct.

In a conical pendulum, when the bob moves in a horizontal circle of radius r, with uniform speed V, the string of length L describe a cone of semi-vertical angle $\theta$. The tension  in the string is given by 

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. $T = \dfrac{mgl}{(L^2 - r^2)}$

  2. $ T = \dfrac{\sqrt {L^2 - r^2}}{mgl}$

  3. $ T = \dfrac{mgL}{\sqrt {L^2 - r^2}}$

  4. $ T = \dfrac{mgL}{(L^2 - r^2)^2}$

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Correct Option: C

A seconds pendulum is attached to roof of car that is moving with acceleration $10{ m/s }^{ 2 }$ a straight road. Its frequency of oscillation 

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. $\dfrac { 1 }{ 2 } Hz$

  2. $1Hz$

  3. $\dfrac { 1 }{ \sqrt { 2 } } Hz$

  4. ${ 2 }^{ -1/4 }Hz$

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Correct Option: D

A simple pendulum in which the bob swings in a horizontal circle is called.

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. Compound pendulum

  2. Horizontal pendulum

  3. Conical pendulum

  4. Gallitzin pendulum

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Correct Option: C

The period of oscillation of a simple pendulum of length $L$ suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination $\boxed { ? } $, is given by

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. $2\pi \sqrt { \dfrac { L }{ gcos\alpha } } $

  2. $2\pi \sqrt { \dfrac { L }{ gsin\alpha } } $

  3. $2\pi \sqrt { \dfrac { L }{ g } } $

  4. $2\pi \sqrt { \dfrac { L }{ gtan\alpha } } $

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Correct Option: A

A simple pendulum of length $40\ cm$ oscillates with an angular amplitude of $0.04\ rad$. Find the speed of the bob when the string makes $0.02 \ rad$ with the vertical. 

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. $4.2\ cm/s$

  2. $3.4\ cm/s$

  3. $6.8\ cm/s$

  4. $13.6\ cm/s$

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Correct Option: C

A metre  stick oscillates  as a compound pendulum  about a horizontal axis  through A Then 

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. the length of an equivalent simple pendulum is 0.58 m

  2. the period of oscillation bout A and B is same

  3. The period of oscillation abut B is approximately 1.52 s

  4. the period of oscillation about A is approximately 2.45 s

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Correct Option: C