Damped Simple Harmonic Motion
PHXI14:OSCILLATIONS

364068 A block of mass \(m\) is connected to a light spring of force constant \(k\). The system is placed inside a damping medium of damping constant \(b\). The instantaneous values of displacement, acceleration and energy of the block are \(x, a\) and \(E\) respectively. The initial amplitude of oscillation is \(A\) and \(\omega^{\prime}\) is the angular frequency of oscillations. The incorrect expression related to the damped oscillations is

1 \(E = \frac{1}{2}k{A^2}{e^{ - \frac{{bt}}{m}}}\)
2 \(m \dfrac{d^{2} x}{d t^{2}}+b \dfrac{d x}{d t}+k x=0\)
3 \(x = A{e^{ - \frac{b}{m}}}\cos \left( {{\omega ^\prime }t + \phi } \right)\)
4 \(\omega^{\prime}=\sqrt{\dfrac{k}{m}-\dfrac{b^{2}}{4 m^{2}}}\)
PHXI14:OSCILLATIONS

364069 Statement A :
In damped oscillations, the energy of the system is dissipated continuously.
Statement B :
For small damping, the energy remains constant.

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

364070 A block of mass \(0.1\;kg\) is connected to an elastic spring of spring constant \(640\,N{m^{ - 1}}\) and oscillates in a damping medium of damping constant \({10^{ - 2}}\;kg\;{s^{ - 1}}\). The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to -

1 \(2\;s\)
2 \(5\;s\)
3 \(7\;s\)
4 \(3.5\;s\)
PHXI14:OSCILLATIONS

364071 In a damped oscillation, damping constant is \(20\,gm/\sec \) and mass of an object is \(500\,gm\). Find out time when amplitude of oscillation becomes half

1 \(34.6\,\sec \)
2 \(44.6\,\sec \)
3 \(65.1\,\sec \)
4 \(55.6\,\sec \)
PHXI14:OSCILLATIONS

364068 A block of mass \(m\) is connected to a light spring of force constant \(k\). The system is placed inside a damping medium of damping constant \(b\). The instantaneous values of displacement, acceleration and energy of the block are \(x, a\) and \(E\) respectively. The initial amplitude of oscillation is \(A\) and \(\omega^{\prime}\) is the angular frequency of oscillations. The incorrect expression related to the damped oscillations is

1 \(E = \frac{1}{2}k{A^2}{e^{ - \frac{{bt}}{m}}}\)
2 \(m \dfrac{d^{2} x}{d t^{2}}+b \dfrac{d x}{d t}+k x=0\)
3 \(x = A{e^{ - \frac{b}{m}}}\cos \left( {{\omega ^\prime }t + \phi } \right)\)
4 \(\omega^{\prime}=\sqrt{\dfrac{k}{m}-\dfrac{b^{2}}{4 m^{2}}}\)
PHXI14:OSCILLATIONS

364069 Statement A :
In damped oscillations, the energy of the system is dissipated continuously.
Statement B :
For small damping, the energy remains constant.

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

364070 A block of mass \(0.1\;kg\) is connected to an elastic spring of spring constant \(640\,N{m^{ - 1}}\) and oscillates in a damping medium of damping constant \({10^{ - 2}}\;kg\;{s^{ - 1}}\). The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to -

1 \(2\;s\)
2 \(5\;s\)
3 \(7\;s\)
4 \(3.5\;s\)
PHXI14:OSCILLATIONS

364071 In a damped oscillation, damping constant is \(20\,gm/\sec \) and mass of an object is \(500\,gm\). Find out time when amplitude of oscillation becomes half

1 \(34.6\,\sec \)
2 \(44.6\,\sec \)
3 \(65.1\,\sec \)
4 \(55.6\,\sec \)
PHXI14:OSCILLATIONS

364068 A block of mass \(m\) is connected to a light spring of force constant \(k\). The system is placed inside a damping medium of damping constant \(b\). The instantaneous values of displacement, acceleration and energy of the block are \(x, a\) and \(E\) respectively. The initial amplitude of oscillation is \(A\) and \(\omega^{\prime}\) is the angular frequency of oscillations. The incorrect expression related to the damped oscillations is

1 \(E = \frac{1}{2}k{A^2}{e^{ - \frac{{bt}}{m}}}\)
2 \(m \dfrac{d^{2} x}{d t^{2}}+b \dfrac{d x}{d t}+k x=0\)
3 \(x = A{e^{ - \frac{b}{m}}}\cos \left( {{\omega ^\prime }t + \phi } \right)\)
4 \(\omega^{\prime}=\sqrt{\dfrac{k}{m}-\dfrac{b^{2}}{4 m^{2}}}\)
PHXI14:OSCILLATIONS

364069 Statement A :
In damped oscillations, the energy of the system is dissipated continuously.
Statement B :
For small damping, the energy remains constant.

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

364070 A block of mass \(0.1\;kg\) is connected to an elastic spring of spring constant \(640\,N{m^{ - 1}}\) and oscillates in a damping medium of damping constant \({10^{ - 2}}\;kg\;{s^{ - 1}}\). The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to -

1 \(2\;s\)
2 \(5\;s\)
3 \(7\;s\)
4 \(3.5\;s\)
PHXI14:OSCILLATIONS

364071 In a damped oscillation, damping constant is \(20\,gm/\sec \) and mass of an object is \(500\,gm\). Find out time when amplitude of oscillation becomes half

1 \(34.6\,\sec \)
2 \(44.6\,\sec \)
3 \(65.1\,\sec \)
4 \(55.6\,\sec \)
PHXI14:OSCILLATIONS

364068 A block of mass \(m\) is connected to a light spring of force constant \(k\). The system is placed inside a damping medium of damping constant \(b\). The instantaneous values of displacement, acceleration and energy of the block are \(x, a\) and \(E\) respectively. The initial amplitude of oscillation is \(A\) and \(\omega^{\prime}\) is the angular frequency of oscillations. The incorrect expression related to the damped oscillations is

1 \(E = \frac{1}{2}k{A^2}{e^{ - \frac{{bt}}{m}}}\)
2 \(m \dfrac{d^{2} x}{d t^{2}}+b \dfrac{d x}{d t}+k x=0\)
3 \(x = A{e^{ - \frac{b}{m}}}\cos \left( {{\omega ^\prime }t + \phi } \right)\)
4 \(\omega^{\prime}=\sqrt{\dfrac{k}{m}-\dfrac{b^{2}}{4 m^{2}}}\)
PHXI14:OSCILLATIONS

364069 Statement A :
In damped oscillations, the energy of the system is dissipated continuously.
Statement B :
For small damping, the energy remains constant.

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

364070 A block of mass \(0.1\;kg\) is connected to an elastic spring of spring constant \(640\,N{m^{ - 1}}\) and oscillates in a damping medium of damping constant \({10^{ - 2}}\;kg\;{s^{ - 1}}\). The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to -

1 \(2\;s\)
2 \(5\;s\)
3 \(7\;s\)
4 \(3.5\;s\)
PHXI14:OSCILLATIONS

364071 In a damped oscillation, damping constant is \(20\,gm/\sec \) and mass of an object is \(500\,gm\). Find out time when amplitude of oscillation becomes half

1 \(34.6\,\sec \)
2 \(44.6\,\sec \)
3 \(65.1\,\sec \)
4 \(55.6\,\sec \)