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1. In the absence of dissipative force, the time period \((T)\) of a simple pendulum (performing oscillations of small amplitude) is: 
1. \(2 \pi \sqrt{\frac{l}{g} } \)
2. \(2 \pi \sqrt{\frac{g}{l}} \)
3 \(\frac{1}{2} \pi \sqrt{\frac{l}{g}}\)
4. \(\frac{1}{2 \pi} \sqrt{\frac{g}{l}}\)

2. In the presence of air resistance, the time period of a simple pendulum ______ with time:
1. increases
2. decreases
3. remains same
4. can't be determined

3. An oscillating system has its energy being dissipated by resistive forces is said to be performing:

1.	forced oscillations
2.	free oscillations
3.	damped oscillations
4.	undamped oscillations

4. If a dissipative force \(\left(F_0\right)\) acts on a particle of mass \(\text { ' } m \text { ' }\)executing SHM of amplitude A such that \(F_0=-b v\) where\(\text { ' } v^{\prime}\) is the velocity of the particle and \(\text { 'b' }\) is a constant then displacement of the particle can be best described by: 
1. \(x(t)=\frac{2 A_m}{b t} \cos (\omega t)\)
2. \(x(t)=\frac{A}{m b t} \cos (\omega t)\)
3. \(x(t)=A e^{-b t / 2 m}\)
4. \(x(t)=A e^{-b t / 2 m}(\cos \omega t)\)

5. If a dissipative force \(\left(F_0\right)\) acts on a particle of mass \(\text { ' } m \text { ' }\)executing SHM of amplitude A such that \(F_0=-b v\) where\(\text { ' } v^{\prime}\) is the velocity of the particle and \(\text { 'b' }\) is a constant then, the variation of energy \(E(t)\) is given by: 
1. \(E(t)=\frac{1}{2} k A^2 \cos ^2 \omega t\)
2. \(E(t)=\frac{1}{2} k A^2 e^{-b t / m}\)
3. \(E(t)=\frac{1}{2} k A^2 e^{b t / m}\)
4. \(E(t)=\frac{1}{2} k A^2 e^{b t / m} \cos ^2 \omega t\)

6. A particle undergoing damped oscillations (with small damping) is said to be performing: 
1. Oscillatory motion 
2. Periodic motion 
3. Simple harmonic motion 
4. Both (1) and (2)

7. The oscillations of a simple pendulum in air is an example of: 
1. Free oscillation
2. Force oscillation
3. Damped oscillation
4. Can either be forced or damped oscillation 

8. In damped oscillations, damping force is directly proportional to speed of the oscillator. If amplitude becomes half of its maximum \(\left(A_0\right)\) value in time \((t)\). then after time \(2 t\), amplitude will be:
1. \(\frac{A_0}{4}\)
2. \(\frac{A_0}{2}\)
3. \(A_0\)
4. \(\frac{\sqrt{3} A_0}{4}\)

9. If a simple pendulum oscillates with small amplitude \(\left(A_0\right)\) then the total energy of oscillations can be given by: 
(symbols have usual meanings)
1. \(\frac{m g A_0^2}{2l}\)
2. \(\frac{m g l}{4 \pi A_0}\)
3. \(\frac{m g A_0^2}{3 l}\)
4. \(\frac{m g A_0^2}{4 \pi^2}\)

10. The amplitude of oscillations is reduced to half of its initial value of \(5 \mathrm{~cm}\) (due to damping by resistive forces) at 
the end of \(25\) oscillations. After it completes \(50\) oscillations its amplitude will be: 
1. \(1.25 \mathrm{~cm}\)
2. \(0.625 \mathrm{~cm}\)
3. \(0.3125 \mathrm{~cm}\)
4. \(0.15625 \mathrm{~cm}\)