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PHXI14:OSCILLATIONS

364148 During the phenomenon of resonance

1 the amplitude of oscillation becomes large

2 the frequency of oscillation becomes large

3 the time period of oscillation becomes large

4 All of the above

PHXI14:OSCILLATIONS

364149 Assertion :
In real situation the amplitude of forced oscillation can never be infinite.
Reason :
The energy of oscillator is continuously dissipated.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

PHXI14:OSCILLATIONS

364150 A particle, with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force, $F = F_{o} \sin ω t$ . If the amplitude of the particle is maximum for $ω = ω_{1}$ and energy of the particle is maximum for $ω = ω_{2}$ , then

1

ω_{1} = ω_{o}

and

ω_{2} = ω_{0}

2

ω_{1} = ω_{o}

and

ω_{2} \neq ω_{o}

3

ω_{1} \neq ω_{o}

and

ω_{2} \neq ω_{o}

4

ω_{1} \neq ω_{o}

and

ω_{2} = ω_{o}

Explanation:

Amplitude resonance takes place at a frequency of external force which is less than the frequency of undamped maximum vibration.
At amplitude resonance $ω_{1} = \sqrt{ω_{o}^{2} - 2 γ^{2}}$
Where $ω_{1}$ during frequency $ω_{1} < ω_{o}$
Velocity-resonance takes place (i.e., maximum energy) when frequency of external periodic force is equal to natural frequency of undamped vibrations.
At velocity resonance $ω_{o} = ω_{2}$
$ω_{2} -$ driving frequency

PHXI14:OSCILLATIONS

364151 A simple harmonic oscillator of angular frequency $2 r a d^{- 1}$ is acted upon by an external force $F = f (t)$ . If the oscillator is at rest in its equilibrium position at $t = 0$ , its position at later times is proportional to :

1

\sin t + \frac{1}{2} \sin 2 t

2

\sin t - \frac{1}{2} \sin 2 t

3

\sin t + \frac{1}{2} \cos 2 t

4

\cos t - \frac{1}{2} \sin 2 t

Explanation:

$x \propto \sin t - \frac{1}{2} \sin 2 t$
$v α \cos t - \cos 2 t$
At $t = 0 x & v$ both have to be zero

JEE - 2014

PHXI14:OSCILLATIONS

364152 A body executes simple harmonic motion under the action of force $F_{1}$ with a time period $\frac{4}{5} s$ . If the force is changed to $F_{2}$ it executes space harmonic motion with time period $\frac{3}{5}$ s. If both forces $F_{1}$ and $F_{2}$ act simultaneously in the same direction on the body then, its time period will be

1

\frac{12}{25} s

2

\frac{24}{25} s

3

\frac{35}{24} s

4

\frac{15}{12} s

Explanation:

The required time period would be given by
$T = T_{1} \times T_{2}$
$[∵$ Time period is multiplicative $]$
$= \frac{4}{5} \times \frac{3}{5} = \frac{12}{25} s$

PHXI14:OSCILLATIONS

364148 During the phenomenon of resonance

1 the amplitude of oscillation becomes large

2 the frequency of oscillation becomes large

3 the time period of oscillation becomes large

4 All of the above

PHXI14:OSCILLATIONS

364149 Assertion :
In real situation the amplitude of forced oscillation can never be infinite.
Reason :
The energy of oscillator is continuously dissipated.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

PHXI14:OSCILLATIONS

364150 A particle, with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force, $F = F_{o} \sin ω t$ . If the amplitude of the particle is maximum for $ω = ω_{1}$ and energy of the particle is maximum for $ω = ω_{2}$ , then

1

ω_{1} = ω_{o}

and

ω_{2} = ω_{0}

2

ω_{1} = ω_{o}

and

ω_{2} \neq ω_{o}

3

ω_{1} \neq ω_{o}

and

ω_{2} \neq ω_{o}

4

ω_{1} \neq ω_{o}

and

ω_{2} = ω_{o}

Explanation:

Amplitude resonance takes place at a frequency of external force which is less than the frequency of undamped maximum vibration.
At amplitude resonance $ω_{1} = \sqrt{ω_{o}^{2} - 2 γ^{2}}$
Where $ω_{1}$ during frequency $ω_{1} < ω_{o}$
Velocity-resonance takes place (i.e., maximum energy) when frequency of external periodic force is equal to natural frequency of undamped vibrations.
At velocity resonance $ω_{o} = ω_{2}$
$ω_{2} -$ driving frequency

PHXI14:OSCILLATIONS

364151 A simple harmonic oscillator of angular frequency $2 r a d^{- 1}$ is acted upon by an external force $F = f (t)$ . If the oscillator is at rest in its equilibrium position at $t = 0$ , its position at later times is proportional to :

1

\sin t + \frac{1}{2} \sin 2 t

2

\sin t - \frac{1}{2} \sin 2 t

3

\sin t + \frac{1}{2} \cos 2 t

4

\cos t - \frac{1}{2} \sin 2 t

Explanation:

$x \propto \sin t - \frac{1}{2} \sin 2 t$
$v α \cos t - \cos 2 t$
At $t = 0 x & v$ both have to be zero

JEE - 2014

PHXI14:OSCILLATIONS

364152 A body executes simple harmonic motion under the action of force $F_{1}$ with a time period $\frac{4}{5} s$ . If the force is changed to $F_{2}$ it executes space harmonic motion with time period $\frac{3}{5}$ s. If both forces $F_{1}$ and $F_{2}$ act simultaneously in the same direction on the body then, its time period will be

1

\frac{12}{25} s

2

\frac{24}{25} s

3

\frac{35}{24} s

4

\frac{15}{12} s

Explanation:

The required time period would be given by
$T = T_{1} \times T_{2}$
$[∵$ Time period is multiplicative $]$
$= \frac{4}{5} \times \frac{3}{5} = \frac{12}{25} s$

PHXI14:OSCILLATIONS

364148 During the phenomenon of resonance

1 the amplitude of oscillation becomes large

2 the frequency of oscillation becomes large

3 the time period of oscillation becomes large

4 All of the above

PHXI14:OSCILLATIONS

364149 Assertion :
In real situation the amplitude of forced oscillation can never be infinite.
Reason :
The energy of oscillator is continuously dissipated.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

PHXI14:OSCILLATIONS

364150 A particle, with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force, $F = F_{o} \sin ω t$ . If the amplitude of the particle is maximum for $ω = ω_{1}$ and energy of the particle is maximum for $ω = ω_{2}$ , then

1

ω_{1} = ω_{o}

and

ω_{2} = ω_{0}

2

ω_{1} = ω_{o}

and

ω_{2} \neq ω_{o}

3

ω_{1} \neq ω_{o}

and

ω_{2} \neq ω_{o}

4

ω_{1} \neq ω_{o}

and

ω_{2} = ω_{o}

Explanation:

Amplitude resonance takes place at a frequency of external force which is less than the frequency of undamped maximum vibration.
At amplitude resonance $ω_{1} = \sqrt{ω_{o}^{2} - 2 γ^{2}}$
Where $ω_{1}$ during frequency $ω_{1} < ω_{o}$
Velocity-resonance takes place (i.e., maximum energy) when frequency of external periodic force is equal to natural frequency of undamped vibrations.
At velocity resonance $ω_{o} = ω_{2}$
$ω_{2} -$ driving frequency

PHXI14:OSCILLATIONS

364151 A simple harmonic oscillator of angular frequency $2 r a d^{- 1}$ is acted upon by an external force $F = f (t)$ . If the oscillator is at rest in its equilibrium position at $t = 0$ , its position at later times is proportional to :

1

\sin t + \frac{1}{2} \sin 2 t

2

\sin t - \frac{1}{2} \sin 2 t

3

\sin t + \frac{1}{2} \cos 2 t

4

\cos t - \frac{1}{2} \sin 2 t

Explanation:

$x \propto \sin t - \frac{1}{2} \sin 2 t$
$v α \cos t - \cos 2 t$
At $t = 0 x & v$ both have to be zero

JEE - 2014

PHXI14:OSCILLATIONS

364152 A body executes simple harmonic motion under the action of force $F_{1}$ with a time period $\frac{4}{5} s$ . If the force is changed to $F_{2}$ it executes space harmonic motion with time period $\frac{3}{5}$ s. If both forces $F_{1}$ and $F_{2}$ act simultaneously in the same direction on the body then, its time period will be

1

\frac{12}{25} s

2

\frac{24}{25} s

3

\frac{35}{24} s

4

\frac{15}{12} s

Explanation:

The required time period would be given by
$T = T_{1} \times T_{2}$
$[∵$ Time period is multiplicative $]$
$= \frac{4}{5} \times \frac{3}{5} = \frac{12}{25} s$

PHXI14:OSCILLATIONS

364148 During the phenomenon of resonance

1 the amplitude of oscillation becomes large

2 the frequency of oscillation becomes large

3 the time period of oscillation becomes large

4 All of the above

PHXI14:OSCILLATIONS

364149 Assertion :
In real situation the amplitude of forced oscillation can never be infinite.
Reason :
The energy of oscillator is continuously dissipated.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

PHXI14:OSCILLATIONS

364150 A particle, with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force, $F = F_{o} \sin ω t$ . If the amplitude of the particle is maximum for $ω = ω_{1}$ and energy of the particle is maximum for $ω = ω_{2}$ , then

1

ω_{1} = ω_{o}

and

ω_{2} = ω_{0}

2

ω_{1} = ω_{o}

and

ω_{2} \neq ω_{o}

3

ω_{1} \neq ω_{o}

and

ω_{2} \neq ω_{o}

4

ω_{1} \neq ω_{o}

and

ω_{2} = ω_{o}

Explanation:

Amplitude resonance takes place at a frequency of external force which is less than the frequency of undamped maximum vibration.
At amplitude resonance $ω_{1} = \sqrt{ω_{o}^{2} - 2 γ^{2}}$
Where $ω_{1}$ during frequency $ω_{1} < ω_{o}$
Velocity-resonance takes place (i.e., maximum energy) when frequency of external periodic force is equal to natural frequency of undamped vibrations.
At velocity resonance $ω_{o} = ω_{2}$
$ω_{2} -$ driving frequency

PHXI14:OSCILLATIONS

364151 A simple harmonic oscillator of angular frequency $2 r a d^{- 1}$ is acted upon by an external force $F = f (t)$ . If the oscillator is at rest in its equilibrium position at $t = 0$ , its position at later times is proportional to :

1

\sin t + \frac{1}{2} \sin 2 t

2

\sin t - \frac{1}{2} \sin 2 t

3

\sin t + \frac{1}{2} \cos 2 t

4

\cos t - \frac{1}{2} \sin 2 t

Explanation:

$x \propto \sin t - \frac{1}{2} \sin 2 t$
$v α \cos t - \cos 2 t$
At $t = 0 x & v$ both have to be zero

JEE - 2014

PHXI14:OSCILLATIONS

364152 A body executes simple harmonic motion under the action of force $F_{1}$ with a time period $\frac{4}{5} s$ . If the force is changed to $F_{2}$ it executes space harmonic motion with time period $\frac{3}{5}$ s. If both forces $F_{1}$ and $F_{2}$ act simultaneously in the same direction on the body then, its time period will be

1

\frac{12}{25} s

2

\frac{24}{25} s

3

\frac{35}{24} s

4

\frac{15}{12} s

Explanation:

The required time period would be given by
$T = T_{1} \times T_{2}$
$[∵$ Time period is multiplicative $]$
$= \frac{4}{5} \times \frac{3}{5} = \frac{12}{25} s$

PHXI14:OSCILLATIONS

364148 During the phenomenon of resonance

1 the amplitude of oscillation becomes large

2 the frequency of oscillation becomes large

3 the time period of oscillation becomes large

4 All of the above

PHXI14:OSCILLATIONS

364149 Assertion :
In real situation the amplitude of forced oscillation can never be infinite.
Reason :
The energy of oscillator is continuously dissipated.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

PHXI14:OSCILLATIONS

364150 A particle, with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force, $F = F_{o} \sin ω t$ . If the amplitude of the particle is maximum for $ω = ω_{1}$ and energy of the particle is maximum for $ω = ω_{2}$ , then

1

ω_{1} = ω_{o}

and

ω_{2} = ω_{0}

2

ω_{1} = ω_{o}

and

ω_{2} \neq ω_{o}

3

ω_{1} \neq ω_{o}

and

ω_{2} \neq ω_{o}

4

ω_{1} \neq ω_{o}

and

ω_{2} = ω_{o}

Explanation:

Amplitude resonance takes place at a frequency of external force which is less than the frequency of undamped maximum vibration.
At amplitude resonance $ω_{1} = \sqrt{ω_{o}^{2} - 2 γ^{2}}$
Where $ω_{1}$ during frequency $ω_{1} < ω_{o}$
Velocity-resonance takes place (i.e., maximum energy) when frequency of external periodic force is equal to natural frequency of undamped vibrations.
At velocity resonance $ω_{o} = ω_{2}$
$ω_{2} -$ driving frequency

PHXI14:OSCILLATIONS

364151 A simple harmonic oscillator of angular frequency $2 r a d^{- 1}$ is acted upon by an external force $F = f (t)$ . If the oscillator is at rest in its equilibrium position at $t = 0$ , its position at later times is proportional to :

1

\sin t + \frac{1}{2} \sin 2 t

2

\sin t - \frac{1}{2} \sin 2 t

3

\sin t + \frac{1}{2} \cos 2 t

4

\cos t - \frac{1}{2} \sin 2 t

Explanation:

$x \propto \sin t - \frac{1}{2} \sin 2 t$
$v α \cos t - \cos 2 t$
At $t = 0 x & v$ both have to be zero

JEE - 2014

PHXI14:OSCILLATIONS

364152 A body executes simple harmonic motion under the action of force $F_{1}$ with a time period $\frac{4}{5} s$ . If the force is changed to $F_{2}$ it executes space harmonic motion with time period $\frac{3}{5}$ s. If both forces $F_{1}$ and $F_{2}$ act simultaneously in the same direction on the body then, its time period will be

1

\frac{12}{25} s

2

\frac{24}{25} s

3

\frac{35}{24} s

4

\frac{15}{12} s

Explanation:

The required time period would be given by
$T = T_{1} \times T_{2}$
$[∵$ Time period is multiplicative $]$
$= \frac{4}{5} \times \frac{3}{5} = \frac{12}{25} s$