Oscillations
- The amplitude of a pendulum executing simple harmonic motion falls to 1/3 the original value after 100 oscillations. The amplitude falls to S times the original value after 200 oscillations, where S is
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In harmonic oscillator, amplitude falls exponentially.
After 100 oscillations amplitude falls to 1 times. 3 ∴ After next 100 oscillations i.e., after 200 oscillations amplitude falls to 
1 
2 = 1 times. 3 9
Correct Option: A
In harmonic oscillator, amplitude falls exponentially.
After 100 oscillations amplitude falls to 1 times. 3 ∴ After next 100 oscillations i.e., after 200 oscillations amplitude falls to 1 2 = 1 times. 3 9
- Resonance is an example of
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We know that if frequency of an external forced oscillation is equal to the natural frequency of the body, then amplitude of the forced oscillation of the body becomes very large. This phenomenon is known as resonant vibration. Therefore, resonance is an example of forced vibration.
Correct Option: B
We know that if frequency of an external forced oscillation is equal to the natural frequency of the body, then amplitude of the forced oscillation of the body becomes very large. This phenomenon is known as resonant vibration. Therefore, resonance is an example of forced vibration.
- In case of a forced vibration, the resonance wave becomes very sharp when the
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The resonance wave becomes very sharp when damping force is small.
Correct Option: B
The resonance wave becomes very sharp when damping force is small.
- The damping force on an oscillator is directly proportional to the velocity. The unit of the constant of proportionality is :
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F ∝ v ⇒ F = kv
k = F ⇒ [k] = | kgms-2 | = kgs-1 v | ms-2 | Correct Option: C
F ∝ v ⇒ F = kv
k = F ⇒ [k] = | kgms-2 | = kgs-1 v | ms-2 |
- A mass m is suspended from a two coupled springs, connected in series. The force constant for springs are k1 and k2. The time period of the suspended mass will be
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The effective spring constant of two springs in series; K = k1 k2 k1 + k2 Time period, T = 2π 
= 2π m m(k1 + k2) K k1 k2 Correct Option: D
The effective spring constant of two springs in series; K = k1 k2 k1 + k2 Time period, T = 2π = 2π m m(k1 + k2) K k1 k2
