Damped Simple Harmonic Motion
PHXI14:OSCILLATIONS

364072 In damped oscillation the amplitude of oscillations is reduced to one-third of its initial value \(a_{0}\) at the end of 100 oscillation. When the oscillation completes 200 oscillations, its amplitude must be

1 \(\dfrac{a_{0}}{4}\)
2 \(\dfrac{a_{0}}{2}\)
3 \(\dfrac{a_{0}}{9}\)
4 \(\dfrac{a_{0}}{6}\)
PHXI14:OSCILLATIONS

364073 If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between \(t=0 s\) to \(t=\tau s\), then \(\tau\) may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity with \(\mathrm{b}\) as the constant of proportionality, the average life time of the pendulum in second is (assuming damping is small) mass of bob is \(m\).

1 \(\dfrac{0.693}{b}\)
2 \(b / m\)
3 \(\dfrac{m}{b}\)
4 \(\dfrac{2 m}{b}\)
PHXI14:OSCILLATIONS

364074 The amplitude of damped oscillator reduced to one-third of its initial value \(A_{0}\) in \(2\;s\). Its amplitude after \(6\;s\) is \(1/n\) times the original. Then \(n\) is equal to

1 \(3^{2}\)
2 \(2^{3}\)
3 \(3^{3}\)
4 \(3^{1 / 3}\)
PHXI14:OSCILLATIONS

364075 Statement A :
Damped oscillation causes loss in energy.
Statement B :
The energy loss in damped oscillation may be due to friction, air resistance etc.

1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
PHXI14:OSCILLATIONS

364072 In damped oscillation the amplitude of oscillations is reduced to one-third of its initial value \(a_{0}\) at the end of 100 oscillation. When the oscillation completes 200 oscillations, its amplitude must be

1 \(\dfrac{a_{0}}{4}\)
2 \(\dfrac{a_{0}}{2}\)
3 \(\dfrac{a_{0}}{9}\)
4 \(\dfrac{a_{0}}{6}\)
PHXI14:OSCILLATIONS

364073 If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between \(t=0 s\) to \(t=\tau s\), then \(\tau\) may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity with \(\mathrm{b}\) as the constant of proportionality, the average life time of the pendulum in second is (assuming damping is small) mass of bob is \(m\).

1 \(\dfrac{0.693}{b}\)
2 \(b / m\)
3 \(\dfrac{m}{b}\)
4 \(\dfrac{2 m}{b}\)
PHXI14:OSCILLATIONS

364074 The amplitude of damped oscillator reduced to one-third of its initial value \(A_{0}\) in \(2\;s\). Its amplitude after \(6\;s\) is \(1/n\) times the original. Then \(n\) is equal to

1 \(3^{2}\)
2 \(2^{3}\)
3 \(3^{3}\)
4 \(3^{1 / 3}\)
PHXI14:OSCILLATIONS

364075 Statement A :
Damped oscillation causes loss in energy.
Statement B :
The energy loss in damped oscillation may be due to friction, air resistance etc.

1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
PHXI14:OSCILLATIONS

364072 In damped oscillation the amplitude of oscillations is reduced to one-third of its initial value \(a_{0}\) at the end of 100 oscillation. When the oscillation completes 200 oscillations, its amplitude must be

1 \(\dfrac{a_{0}}{4}\)
2 \(\dfrac{a_{0}}{2}\)
3 \(\dfrac{a_{0}}{9}\)
4 \(\dfrac{a_{0}}{6}\)
PHXI14:OSCILLATIONS

364073 If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between \(t=0 s\) to \(t=\tau s\), then \(\tau\) may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity with \(\mathrm{b}\) as the constant of proportionality, the average life time of the pendulum in second is (assuming damping is small) mass of bob is \(m\).

1 \(\dfrac{0.693}{b}\)
2 \(b / m\)
3 \(\dfrac{m}{b}\)
4 \(\dfrac{2 m}{b}\)
PHXI14:OSCILLATIONS

364074 The amplitude of damped oscillator reduced to one-third of its initial value \(A_{0}\) in \(2\;s\). Its amplitude after \(6\;s\) is \(1/n\) times the original. Then \(n\) is equal to

1 \(3^{2}\)
2 \(2^{3}\)
3 \(3^{3}\)
4 \(3^{1 / 3}\)
PHXI14:OSCILLATIONS

364075 Statement A :
Damped oscillation causes loss in energy.
Statement B :
The energy loss in damped oscillation may be due to friction, air resistance etc.

1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
PHXI14:OSCILLATIONS

364072 In damped oscillation the amplitude of oscillations is reduced to one-third of its initial value \(a_{0}\) at the end of 100 oscillation. When the oscillation completes 200 oscillations, its amplitude must be

1 \(\dfrac{a_{0}}{4}\)
2 \(\dfrac{a_{0}}{2}\)
3 \(\dfrac{a_{0}}{9}\)
4 \(\dfrac{a_{0}}{6}\)
PHXI14:OSCILLATIONS

364073 If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between \(t=0 s\) to \(t=\tau s\), then \(\tau\) may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity with \(\mathrm{b}\) as the constant of proportionality, the average life time of the pendulum in second is (assuming damping is small) mass of bob is \(m\).

1 \(\dfrac{0.693}{b}\)
2 \(b / m\)
3 \(\dfrac{m}{b}\)
4 \(\dfrac{2 m}{b}\)
PHXI14:OSCILLATIONS

364074 The amplitude of damped oscillator reduced to one-third of its initial value \(A_{0}\) in \(2\;s\). Its amplitude after \(6\;s\) is \(1/n\) times the original. Then \(n\) is equal to

1 \(3^{2}\)
2 \(2^{3}\)
3 \(3^{3}\)
4 \(3^{1 / 3}\)
PHXI14:OSCILLATIONS

364075 Statement A :
Damped oscillation causes loss in energy.
Statement B :
The energy loss in damped oscillation may be due to friction, air resistance etc.

1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.