Tag: example of simple harmonic motion

Questions Related to example of simple harmonic motion

A spring of spring constant $k$ is cut into $3$ equal part find $k$ of each

physics oscillatory motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

  1. $3k$

  2. $\dfrac{k}{3}$

  3. $k$

  4. None of these

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Correct Option: A

A body of mass 'm' is suspended with an ideal spring of force constant 'k'. The expected change in the position of the body, due to an additional force 'F' acting vertically downwards is 

physics simple harmonic motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

  1. $\cfrac { 3F }{ 2K } $

  2. $\cfrac { 2F }{ K } $

  3. $\cfrac { 5F }{ 2K } $

  4. $\cfrac { 4F }{ K } $

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Correct Option: B

A block of mass m is suddenly released from the top of a string of stiffness constant k.
(i) The maximum compression in the spring will be
(ii) at equilibrium, the compression in the spring will be .......... 

physics oscillatory motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

  1. 2mg/k, mg/k

  2. mg/k, mg/k

  3. mg/k, 2mg/k

  4. 2mg/k, 2mg/k

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Correct Option: A

A body of $100 gm$ is attached to a spring balance suspended from the celling of an elevator. If the elevator cable breaks and itt falls freely down, the weight of the body as indicated by the spring balance would be $10gm$.

physics oscillatory motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

  1. $10gm$

  2. $0gm$

  3. $1gm$

  4. $None$

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Correct Option: A

A block of mass $m$ moving with speed v compresses a spring through distance $x$ before is halved. What is the value of spring constant?

physics oscillatory motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

  1. $\dfrac { 3 m v ^ { 2 } } { 4 x ^ { 2 } }$

  2. $\dfrac { m v ^ { 2 } } { 4 x ^ { 2 } }$

  3. $\dfrac { m v ^ { 2 } } { 2 x ^ { 2 } }$

  4. $\dfrac { 2 m v ^ { 2 } } { x ^ { 2 } }$

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Correct Option: A
Explanation:

Let the velocity at starting is $v$.

After compression change in velocity $ = \dfrac{v}{2}$
Here, Initial kinetic energy of a block $ = \left( {\dfrac{1}{2}} \right)m{v^2}$
After compression of spring,
Total energy at the point $x$= Kinetic energy of a block +Potential Energy which stored in the spring.
$\begin{array}{l} \left( { \dfrac { 1 }{ 2 }  } \right) m{ v^{ 2 } }=\dfrac { 1 }{ 2 } m{ \left( { \dfrac { v }{ 2 }  } \right) ^{ 2 } }+\dfrac { 1 }{ 2 } k{ v^{ 2 } } \ \dfrac { 1 }{ 2 } k{ v^{ 2 } }=\dfrac { 1 }{ 2 } m{ \left( { \dfrac { v }{ 2 }  } \right) ^{ 2 } }-\dfrac { 1 }{ 2 } \left( { m{ v^{ 2 } } } \right)  \ k{ x^{ 2 } }=m\left( { { v^{ 2 } }-\dfrac { { { v^{ 2 } } } }{ 4 }  } \right)  \ k{ x^{ 2 } }=\dfrac { { 3m{ v^{ ^{ 2 } } } } }{ 4 }  \ \therefore k=\dfrac { { 3m{ v^{ ^{ 2 } } } } }{ { 4{ x^{ 2 } } } }  \end{array}$

A hollow pipe of length $0.8\ m$ is closed at one end. At its open end, a $0.5\ m$ long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $50\ N$ and the speed of sound is $320\ ms^{-1}$, the mass of the string is

physics oscillatory motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

  1. $5\ grams$

  2. $10\ grams$

  3. $20\ grams$

  4. $40\ grams$

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Correct Option: B
Explanation:

Velocity of sound $= c$

$\dfrac{c}{4L} = \dfrac{2v}{l}$

$\Rightarrow \dfrac{320}{4\times 0.8} = \dfrac{1}{5} \sqrt{\dfrac{T}{\mu}}$

$\Rightarrow \mu = 0.02\space kgm^{-1}$

$\Rightarrow m = \mu l = 10\space g $

 

Two blocks are connected to an ideal spring (K = 200 N/m) and placed on a smooth surface. Initially spring is in its natural lenght and blocks are projected as shown. The maximum extension in the spring will be

physics oscillatory motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

  1. 30 cm

  2. 25 cm

  3. 20 cm

  4. 15 cm

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Correct Option: A

Will it make any difference in the extension of the spring, if 3 springs of spring constant k are joined in series to life a load W as compared to one string of spring constant k to lift the same load

physics oscillatory motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

  1. Extension in long spring < extension in shorter spring

  2. Extension in long spring > extension in shorter spring

  3. Extension in both the springs are same

  4. None of the above

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Correct Option: A
Explanation:

If three springs are joined together, their effective spring constant will be k/3. Since load is W, we can write $W=(k/3)x _1$.

If these strings are replaced by a long spring of spring constant k, let the extension of the load be W, we can still write $W=kx _2$

Comparing these two equations, we get, $x _2=x _1/3$ or the extension in the long spring is less than the shorter springs

How many identical springs of spring constant k should be joined in series, so the effective spring constant is k/2

physics oscillatory motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

  1. 8

  2. 4

  3. 1

  4. 2

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Correct Option: D
Explanation:

effective spring constant will be $K _{eff}=(k)(k)/(k+k)=k/2$

The correct answer is option(d)

If two springs of spring constants $k _1$ and $k _2$ whose extensions upon applying a force F are $x _1$ and $x _2$ respectively are joined together in a series configuration, the net extension will be 

physics oscillatory motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

  1. $x= F(1/k _1+1/k _2)$

  2. $x= F(1/k _1-1/k _2)$

  3. $x= F(k _1+k _2)$

  4. $x= F(k _1-k _2)$

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Correct Option: A
Explanation:

$x _1 = F/k _1$ and $x _2=F/k _2$

Upon joining both the springs together, the net extension will be $x =x _1+x _2$

Substituting, we get, $x= F(1/k _1+1/k _2)$

The correct option is (a)