Damped Simple Harmonic Motion
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PHXI14:OSCILLATIONS

364076 A damped harmonic oscillator consists of a block \((m = 2.00\;kg)\), a spring \((k = 10.0\;N/m)\,(k = 10.0\;N/m)\), and a damping force \(F = - bv\), it oscillates with an amplitude of \(25.0\;cm\)' because of the damping, the amplitude falls to three-fourth of this initial value at the completion of four seconds. What is the value of \(b\) ?

1 \(\ln \left( {\frac{4}{3}} \right)kg/s\)
2 \(\ln \left( {\frac{3}{2}} \right)kg/s\)
3 \(2\;kg/s\)
4 \(2\ln 3\;kg/s\)
PHXI14:OSCILLATIONS

364077 Statement A :
In damped oscillations, the total mechanical energy remain constant.
Statement B :
Total mechanical energy of oscillation executing SHM is given by \(\dfrac{1}{2} k A^{2}\), where \(A\) is amplitude at time \(t\).

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

364078 Which of the following quantity does not change due to damping of oscillations?

1 Angular frequency
2 Time period
3 Initial phase
4 Amplitude
PHXI14:OSCILLATIONS

364079 The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are

1 \(kgs\)
2 \(kgm{s^{ - 1}}\)
3 \(kgm{s^{ - 2}}\)
4 \(kg{s^{ - 1}}\)
PHXI14:OSCILLATIONS

364080 The equation of a damped simple harmonic motion is \(m \dfrac{d^{2} x}{d t^{2}}+b \dfrac{d x}{d t}+k x=0\). Then, the angular frequency of oscillation is

1 \(\omega^{\prime}=\left(\dfrac{k}{m}-\dfrac{b^{2}}{4 m^{2}}\right)^{1 / 2}\)
2 \(\omega^{\prime}=\left(\dfrac{k}{m}-\dfrac{b}{4 m}\right)^{1 / 2}\)
3 \(\omega^{\prime}=\left(\dfrac{k}{m}-\dfrac{b^{2}}{4 m}\right)^{1 / 2}\)
4 \(\omega^{\prime}=\left(\dfrac{k}{m}-\dfrac{b^{2}}{4 m^{2}}\right)\)
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PHXI14:OSCILLATIONS

364076 A damped harmonic oscillator consists of a block \((m = 2.00\;kg)\), a spring \((k = 10.0\;N/m)\,(k = 10.0\;N/m)\), and a damping force \(F = - bv\), it oscillates with an amplitude of \(25.0\;cm\)' because of the damping, the amplitude falls to three-fourth of this initial value at the completion of four seconds. What is the value of \(b\) ?

1 \(\ln \left( {\frac{4}{3}} \right)kg/s\)
2 \(\ln \left( {\frac{3}{2}} \right)kg/s\)
3 \(2\;kg/s\)
4 \(2\ln 3\;kg/s\)
PHXI14:OSCILLATIONS

364077 Statement A :
In damped oscillations, the total mechanical energy remain constant.
Statement B :
Total mechanical energy of oscillation executing SHM is given by \(\dfrac{1}{2} k A^{2}\), where \(A\) is amplitude at time \(t\).

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

364078 Which of the following quantity does not change due to damping of oscillations?

1 Angular frequency
2 Time period
3 Initial phase
4 Amplitude
PHXI14:OSCILLATIONS

364079 The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are

1 \(kgs\)
2 \(kgm{s^{ - 1}}\)
3 \(kgm{s^{ - 2}}\)
4 \(kg{s^{ - 1}}\)
PHXI14:OSCILLATIONS

364080 The equation of a damped simple harmonic motion is \(m \dfrac{d^{2} x}{d t^{2}}+b \dfrac{d x}{d t}+k x=0\). Then, the angular frequency of oscillation is

1 \(\omega^{\prime}=\left(\dfrac{k}{m}-\dfrac{b^{2}}{4 m^{2}}\right)^{1 / 2}\)
2 \(\omega^{\prime}=\left(\dfrac{k}{m}-\dfrac{b}{4 m}\right)^{1 / 2}\)
3 \(\omega^{\prime}=\left(\dfrac{k}{m}-\dfrac{b^{2}}{4 m}\right)^{1 / 2}\)
4 \(\omega^{\prime}=\left(\dfrac{k}{m}-\dfrac{b^{2}}{4 m^{2}}\right)\)
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PHXI14:OSCILLATIONS

364076 A damped harmonic oscillator consists of a block \((m = 2.00\;kg)\), a spring \((k = 10.0\;N/m)\,(k = 10.0\;N/m)\), and a damping force \(F = - bv\), it oscillates with an amplitude of \(25.0\;cm\)' because of the damping, the amplitude falls to three-fourth of this initial value at the completion of four seconds. What is the value of \(b\) ?

1 \(\ln \left( {\frac{4}{3}} \right)kg/s\)
2 \(\ln \left( {\frac{3}{2}} \right)kg/s\)
3 \(2\;kg/s\)
4 \(2\ln 3\;kg/s\)
PHXI14:OSCILLATIONS

364077 Statement A :
In damped oscillations, the total mechanical energy remain constant.
Statement B :
Total mechanical energy of oscillation executing SHM is given by \(\dfrac{1}{2} k A^{2}\), where \(A\) is amplitude at time \(t\).

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

364078 Which of the following quantity does not change due to damping of oscillations?

1 Angular frequency
2 Time period
3 Initial phase
4 Amplitude
PHXI14:OSCILLATIONS

364079 The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are

1 \(kgs\)
2 \(kgm{s^{ - 1}}\)
3 \(kgm{s^{ - 2}}\)
4 \(kg{s^{ - 1}}\)
PHXI14:OSCILLATIONS

364080 The equation of a damped simple harmonic motion is \(m \dfrac{d^{2} x}{d t^{2}}+b \dfrac{d x}{d t}+k x=0\). Then, the angular frequency of oscillation is

1 \(\omega^{\prime}=\left(\dfrac{k}{m}-\dfrac{b^{2}}{4 m^{2}}\right)^{1 / 2}\)
2 \(\omega^{\prime}=\left(\dfrac{k}{m}-\dfrac{b}{4 m}\right)^{1 / 2}\)
3 \(\omega^{\prime}=\left(\dfrac{k}{m}-\dfrac{b^{2}}{4 m}\right)^{1 / 2}\)
4 \(\omega^{\prime}=\left(\dfrac{k}{m}-\dfrac{b^{2}}{4 m^{2}}\right)\)
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PHXI14:OSCILLATIONS

364076 A damped harmonic oscillator consists of a block \((m = 2.00\;kg)\), a spring \((k = 10.0\;N/m)\,(k = 10.0\;N/m)\), and a damping force \(F = - bv\), it oscillates with an amplitude of \(25.0\;cm\)' because of the damping, the amplitude falls to three-fourth of this initial value at the completion of four seconds. What is the value of \(b\) ?

1 \(\ln \left( {\frac{4}{3}} \right)kg/s\)
2 \(\ln \left( {\frac{3}{2}} \right)kg/s\)
3 \(2\;kg/s\)
4 \(2\ln 3\;kg/s\)
PHXI14:OSCILLATIONS

364077 Statement A :
In damped oscillations, the total mechanical energy remain constant.
Statement B :
Total mechanical energy of oscillation executing SHM is given by \(\dfrac{1}{2} k A^{2}\), where \(A\) is amplitude at time \(t\).

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

364078 Which of the following quantity does not change due to damping of oscillations?

1 Angular frequency
2 Time period
3 Initial phase
4 Amplitude
PHXI14:OSCILLATIONS

364079 The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are

1 \(kgs\)
2 \(kgm{s^{ - 1}}\)
3 \(kgm{s^{ - 2}}\)
4 \(kg{s^{ - 1}}\)
PHXI14:OSCILLATIONS

364080 The equation of a damped simple harmonic motion is \(m \dfrac{d^{2} x}{d t^{2}}+b \dfrac{d x}{d t}+k x=0\). Then, the angular frequency of oscillation is

1 \(\omega^{\prime}=\left(\dfrac{k}{m}-\dfrac{b^{2}}{4 m^{2}}\right)^{1 / 2}\)
2 \(\omega^{\prime}=\left(\dfrac{k}{m}-\dfrac{b}{4 m}\right)^{1 / 2}\)
3 \(\omega^{\prime}=\left(\dfrac{k}{m}-\dfrac{b^{2}}{4 m}\right)^{1 / 2}\)
4 \(\omega^{\prime}=\left(\dfrac{k}{m}-\dfrac{b^{2}}{4 m^{2}}\right)\)
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PHXI14:OSCILLATIONS

364076 A damped harmonic oscillator consists of a block \((m = 2.00\;kg)\), a spring \((k = 10.0\;N/m)\,(k = 10.0\;N/m)\), and a damping force \(F = - bv\), it oscillates with an amplitude of \(25.0\;cm\)' because of the damping, the amplitude falls to three-fourth of this initial value at the completion of four seconds. What is the value of \(b\) ?

1 \(\ln \left( {\frac{4}{3}} \right)kg/s\)
2 \(\ln \left( {\frac{3}{2}} \right)kg/s\)
3 \(2\;kg/s\)
4 \(2\ln 3\;kg/s\)
PHXI14:OSCILLATIONS

364077 Statement A :
In damped oscillations, the total mechanical energy remain constant.
Statement B :
Total mechanical energy of oscillation executing SHM is given by \(\dfrac{1}{2} k A^{2}\), where \(A\) is amplitude at time \(t\).

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

364078 Which of the following quantity does not change due to damping of oscillations?

1 Angular frequency
2 Time period
3 Initial phase
4 Amplitude
PHXI14:OSCILLATIONS

364079 The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are

1 \(kgs\)
2 \(kgm{s^{ - 1}}\)
3 \(kgm{s^{ - 2}}\)
4 \(kg{s^{ - 1}}\)
PHXI14:OSCILLATIONS

364080 The equation of a damped simple harmonic motion is \(m \dfrac{d^{2} x}{d t^{2}}+b \dfrac{d x}{d t}+k x=0\). Then, the angular frequency of oscillation is

1 \(\omega^{\prime}=\left(\dfrac{k}{m}-\dfrac{b^{2}}{4 m^{2}}\right)^{1 / 2}\)
2 \(\omega^{\prime}=\left(\dfrac{k}{m}-\dfrac{b}{4 m}\right)^{1 / 2}\)
3 \(\omega^{\prime}=\left(\dfrac{k}{m}-\dfrac{b^{2}}{4 m}\right)^{1 / 2}\)
4 \(\omega^{\prime}=\left(\dfrac{k}{m}-\dfrac{b^{2}}{4 m^{2}}\right)\)