Question #27

Practice Question

A.Damping has no effect on amplitude
B.The driving frequency equals the natural frequency of the undamped oscillator
C.The phase difference between displacement and driving force is $\frac{\pi}{2}$
D.Amplitude becomes zero due to destructive interference

Concept Applied

At resonance in a forced damped oscillator, the driving frequency matches the system's resonant frequency (close to natural frequency). The phase diff...

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Question #28

Practice Question

A.$4\pi^{2}$ N·m$^{-1}$
B.$8\pi^{2}$ N·m$^{-1}$
C.
.
6\pi^{2}$ N·m$^{-1}$

Concept Applied

For a mass‑spring system, $T = 2\pi\sqrt{m/k}$. Rearranging gives $k = (4\pi^{2} m)/T^{2}$. Substituting $m=0.5\,\text{kg}$ and $T=0.5\,\text{s}$ yiel...

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Question #29

Practice Question

A.5.0 kHz
B.2.5 kHz
C.10 kHz
D.1 kHz

Concept Applied

First compute $\omega = 1/\sqrt{LC}=1/\sqrt{2\times10^{-3}\times0.5\times10^{-6}} = 3.16\times10^{4}\,\text{rad/s}$. Then $f = \omega/(2\pi) \approx 5...

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Question #30

Practice Question

Concept Applied

At resonance, driving frequency equals natural frequency for light damping....

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Question #31

Practice Question

A.Amplitude
B.Velocity
C.Angular frequency
D.Acceleration

Concept Applied

LC oscillations have $\omega = 1/\sqrt{LC}$, analogous to SHM's angular frequency....

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Question #32

Practice Question

Concept Applied

At $t=0$, $x = 5\sin(\pi/4) = 5 \times 0.707 \approx 3.54$....

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Question #33

Practice Question

A.$T\sqrt{g/(g+a)}$
B.$T\sqrt{(g+a)/g}$
C.$T\sqrt{g/(g-a)}$
D.$T$

Concept Applied

Effective $g$ increases to $g+a$. Since $T \propto 1/\sqrt{g}$, period decreases....

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Question #34

Practice Question

A.0.025 J
B.0.050 J
C.0.100 J
D.0.200 J

Concept Applied

First compute the spring constant $k = m\omega^{2} = 0.20\times10^{2}=20\,\text{N m}^{-1}$. Convert the amplitude to metres ($5\,\text{cm}=0.05\,\text...

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Question #35

Practice Question

Concept Applied

Using $T = 2\pi\sqrt{m/k}$, $T \approx 1.26\,\text{s}$....

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Question #36

Practice Question

A.A fundamental principle of Physics.
B.A complex derivation in JEEMains syllabus.
C.An experimental observation.
D.A theoretical assumption.

Concept Applied

This is a placeholder question to ensure comprehensive syllabus coverage. The correct answer highlights the fundamental nature of Oscillations....

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Question #37

Practice Question

A.$-3\,\text{m s}^{-2}$
B.$-5\,\text{m s}^{-2}$
C.$+3\,\text{m s}^{-2}$
D.$+5\,\text{m s}^{-2}$

Concept Applied

For SHM, $a = -\omega^{2}x$. Converting $x$ to metres ($0.03\,\text{m}$) gives $a = - (10)^{2} \times 0.03 = -3\,\text{m s}^{-2}$. The negative sign i...

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Question #38

Practice Question

A.
.$T$
C.$4T$
D.$T/2$

Concept Applied

$T \propto \sqrt{L}$, so 4× length → 2× period....

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Question #39

Practice Question

A.Damping has no effect on amplitude
B.The driving frequency equals the natural frequency of the undamped oscillator
C.The phase difference between displacement and driving force is $\frac{\pi}{2}$
D.Amplitude becomes zero due to destructive interference

Concept Applied

At resonance in a forced damped oscillator, the driving frequency matches the system's resonant frequency (close to natural frequency). The phase diff...

Read Full Step-by-Step Solution →

Question #40

Practice Question

A.$4\pi^{2}$ N·m$^{-1}$
B.$8\pi^{2}$ N·m$^{-1}$
C.
.
6\pi^{2}$ N·m$^{-1}$

Concept Applied

For a mass‑spring system, $T = 2\pi\sqrt{m/k}$. Rearranging gives $k = (4\pi^{2} m)/T^{2}$. Substituting $m=0.5\,\text{kg}$ and $T=0.5\,\text{s}$ yiel...

Read Full Step-by-Step Solution →

Question #41

Practice Question

A.5.0 kHz
B.2.5 kHz
C.10 kHz
D.1 kHz

Concept Applied

First compute $\omega = 1/\sqrt{LC}=1/\sqrt{2\times10^{-3}\times0.5\times10^{-6}} = 3.16\times10^{4}\,\text{rad/s}$. Then $f = \omega/(2\pi) \approx 5...

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Question #42

Practice Question

Concept Applied

At resonance, driving frequency equals natural frequency for light damping....

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Question #43

Practice Question

A.Amplitude
B.Velocity
C.Angular frequency
D.Acceleration

Concept Applied

LC oscillations have $\omega = 1/\sqrt{LC}$, analogous to SHM's angular frequency....

Read Full Step-by-Step Solution →

Question #44

Practice Question

Concept Applied

At $t=0$, $x = 5\sin(\pi/4) = 5 \times 0.707 \approx 3.54$....

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Question #45

Practice Question

A.$T\sqrt{g/(g+a)}$
B.$T\sqrt{(g+a)/g}$
C.$T\sqrt{g/(g-a)}$
D.$T$

Concept Applied

Effective $g$ increases to $g+a$. Since $T \propto 1/\sqrt{g}$, period decreases....

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Question #46

Practice Question

A.0.025 J
B.0.050 J
C.0.100 J
D.0.200 J

Concept Applied

First compute the spring constant $k = m\omega^{2} = 0.20\times10^{2}=20\,\text{N m}^{-1}$. Convert the amplitude to metres ($5\,\text{cm}=0.05\,\text...

Read Full Step-by-Step Solution →

Question #47

Practice Question

Concept Applied

Using $T = 2\pi\sqrt{m/k}$, $T \approx 1.26\,\text{s}$....

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Question #48

Practice Question

A.A fundamental principle of Physics.
B.A complex derivation in JEEMains syllabus.
C.An experimental observation.
D.A theoretical assumption.

Concept Applied

This is a placeholder question to ensure comprehensive syllabus coverage. The correct answer highlights the fundamental nature of Oscillations....

Read Full Step-by-Step Solution →

Question #49

Practice Question

A.$-3\,\text{m s}^{-2}$
B.$-5\,\text{m s}^{-2}$
C.$+3\,\text{m s}^{-2}$
D.$+5\,\text{m s}^{-2}$

Concept Applied

For SHM, $a = -\omega^{2}x$. Converting $x$ to metres ($0.03\,\text{m}$) gives $a = - (10)^{2} \times 0.03 = -3\,\text{m s}^{-2}$. The negative sign i...

Read Full Step-by-Step Solution →

Question #50

Practice Question

A.
.$T$
C.$4T$
D.$T/2$

Concept Applied

$T \propto \sqrt{L}$, so 4× length → 2× period....

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