Tag: resonance

Questions Related to resonance

Undamped oscillations are practically impossible because

physics option b: engineering physics introduction to sound free, forced and damped oscillations resonance

  1. there is always loss of energy.

  2. there is no force opposing friction.

  3. energy is not conserved in such oscillations.

  4. None of these.

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Correct Option: A
Explanation:

Underdamped oscillation is practical because there always be resistive force present in reality which will try to make an oscillating body to lose its energy. This loss of energy makes the motion damped motion.

Dampers are found on bridges

physics option b: engineering physics introduction to sound free, forced and damped oscillations resonance

  1. to allow natural oscillations to occur.

  2. to prevent them from swaying due to wind.

  3. to prevent resonance of frequencies.

  4. None of these.

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Correct Option: B
Explanation:

Dampers are found bridges to prevent them from swaying due to wind otherwise this motion can hamper the condition of a bridge.

If we wish to represent the equation for the position of the mass in terms of a differential equation, which one of these would be the most suitable?

physics option b: engineering physics introduction to sound free, forced and damped oscillations resonance

  1. $ m \dfrac{d^2x}{dt^2} + b \dfrac{dx}{dt} + kx = 0$

  2. $ m \dfrac{d^2x}{dt^2} - b \dfrac{dx}{dt} + kx = 0$

  3. $ m \dfrac{d^2x}{dt^2} + b \dfrac{dx}{dt} - kx = 0$

  4. $ m \dfrac{d^2x}{dt^2} -b \dfrac{dx}{dt} - kx = 0$

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Correct Option: A
Explanation:

The force on body oscillating in resistive medium is 

$f = -kx - bv$
$\Rightarrow m\dfrac { { d }^{ 2 }x }{ d{ t }^{ 2 } } =-kx-b\dfrac { dx }{ dt } \ \Rightarrow m\dfrac { { d }^{ 2 }x }{ d{ t }^{ 2 } } +b\dfrac { dx }{ dt } +kx=0$
k = oscillating constant 
x = displacement of body from mean position 
b = constant depends on resistive medium 
v = velocity of object = $\dfrac{dx}{dt}$
m = mass of object .

Two point masses $m _1$ and $m _2$ are coupled by a spring of spring. Constant $k$ and uncompressed length $L _0$. The spring is fully compressed and a thread ties the masses together with negligible separation between them. The tied assembly is moving in the $+x$ direction with uniform speed $v _0$. At a time, say $t = 0$, it is passing the origin and at that instant the thread breaks. The masses, attached to the spring, start oscillating. The displacement of mass $m _1$ given by $x _1(t) = v _0 t(1 - cos \omega t)$ where $A$ is a constant. Find (i) the displacement $x _2(t)$ is $m _2$, and (ii) the relationship between $A$ and $L _0$.

physics oscillations introduction to sound free, forced and damped oscillations resonance

  1. (i) $v _0 t + \dfrac{m _1}{2m _2}A(1 - cos \omega t)$

    (ii) $A = \left(\dfrac{m _2}{2m _1 + m _2}\right)$

  2. (i) $v _0 t + \dfrac{m _1}{m _2}A(1 - cos \omega t)$

    (ii) $A = \left(\dfrac{m _2}{m _1 + m _2}\right)$

  3. (i) $v _0 t + \dfrac{m _1}{3m _2}A(1 - cos \omega t)$

    (ii) $A = \left(\dfrac{m _2}{3m _1 + m _2}\right)$

  4. (i) $v _0 t + \dfrac{m _1}{4m _2}A(1 - cos \omega t)$

    (ii) $A = \left(\dfrac{m _2}{4m _1 + m _2}\right)$

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Correct Option: B

To and fro motion of a particle about its mean position is called -

physics propagation of sound waves introduction to sound free, forced and damped oscillations resonance

  1. frequency

  2. amplitude

  3. vibration

  4. acceleration

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Correct Option: C
Explanation:

To and fro motion of a particle about mean position is called vibrational motion.

The time taken by a vibrating body to complete one vibration is called its frequency. True or false.

physics propagation of sound waves introduction to sound free, forced and damped oscillations resonance

  1. True

  2. False

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Correct Option: B
Explanation:

The time taken by vibrating body to complete one vibration is called time period. so our given statement is false.