Force and Damped Oscillation, Resonance
Oscillations

140807 A small block of mass $100 \mathrm{~g}$ is tied to a spring of spring constant $7.5 \mathrm{~N} / \mathrm{m}$ and length $20 \mathrm{~cm}$. the other end of spring is fixed at a particular point $A$. If the block moves in a circular path on a smooth horizontal surface with constant angular velocity $5 \mathrm{rad} / \mathrm{s}$ about point $A$, then tension in the spring is

1 $1.5 \mathrm{~N}$
2 $0.75 \mathrm{~N}$
3 $0.25 \mathrm{~N}$
4 $0.50 \mathrm{~N}$
Oscillations

140808 If the amplitude of a lightly damped oscillator decreases by $1.5 \%$ then the mechanical energy of the oscillator lost in each cycle is

1 $1.5 \%$
2 $0.75 \%$
3 $6 \%$
4 $3 \%$
Oscillations

140809 The amplitude of a damped oscillator varies with time as $A(t)=A_{0} \exp (-b t / 2 m)$ where $b=$ $70 \mathrm{~g} / \mathrm{s}$ and $\mathrm{m}=200 \mathrm{~g}$. How long does it take for the mechanical energy to drop to one - fourth of its initial value?
[Take $\ln 2=0.7]$

1 $2.0 \mathrm{~s}$
2 $4.0 \mathrm{~s}$
3 $2.5 \mathrm{~s}$
4 $3.5 \mathrm{~s}$
Oscillations

140810 The amplitude of a damped oscillator is known to decreases to 0.9 times its original magnitude in 5 seconds. Approximately, by how many times its original magnitude will its amplitude decrease after another 10 seconds?

1 0.73
2 0.9
3 0.59
4 0.26
Oscillations

140811 A particle of mass ' $m$ ' is under an influence of a force $\overrightarrow{\mathbf{F}}=-\mathbf{k} \overrightarrow{\mathbf{x}}+\overrightarrow{\mathbf{F}}_{0}$. The particle when disturbed will oscillate

1 About $x=0$ with $\omega=\sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$
2 About $x=0$ with $\omega=\sqrt{\frac{m}{k}}$
3 About $\mathrm{x}=\frac{\mathrm{F}_{0}}{\mathrm{k}}$ with $\omega=\sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$
4 About $\mathrm{x}=\frac{\mathrm{F}_{0}}{\mathrm{k}}$ with $\omega \neq \sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$
Oscillations

140807 A small block of mass $100 \mathrm{~g}$ is tied to a spring of spring constant $7.5 \mathrm{~N} / \mathrm{m}$ and length $20 \mathrm{~cm}$. the other end of spring is fixed at a particular point $A$. If the block moves in a circular path on a smooth horizontal surface with constant angular velocity $5 \mathrm{rad} / \mathrm{s}$ about point $A$, then tension in the spring is

1 $1.5 \mathrm{~N}$
2 $0.75 \mathrm{~N}$
3 $0.25 \mathrm{~N}$
4 $0.50 \mathrm{~N}$
Oscillations

140808 If the amplitude of a lightly damped oscillator decreases by $1.5 \%$ then the mechanical energy of the oscillator lost in each cycle is

1 $1.5 \%$
2 $0.75 \%$
3 $6 \%$
4 $3 \%$
Oscillations

140809 The amplitude of a damped oscillator varies with time as $A(t)=A_{0} \exp (-b t / 2 m)$ where $b=$ $70 \mathrm{~g} / \mathrm{s}$ and $\mathrm{m}=200 \mathrm{~g}$. How long does it take for the mechanical energy to drop to one - fourth of its initial value?
[Take $\ln 2=0.7]$

1 $2.0 \mathrm{~s}$
2 $4.0 \mathrm{~s}$
3 $2.5 \mathrm{~s}$
4 $3.5 \mathrm{~s}$
Oscillations

140810 The amplitude of a damped oscillator is known to decreases to 0.9 times its original magnitude in 5 seconds. Approximately, by how many times its original magnitude will its amplitude decrease after another 10 seconds?

1 0.73
2 0.9
3 0.59
4 0.26
Oscillations

140811 A particle of mass ' $m$ ' is under an influence of a force $\overrightarrow{\mathbf{F}}=-\mathbf{k} \overrightarrow{\mathbf{x}}+\overrightarrow{\mathbf{F}}_{0}$. The particle when disturbed will oscillate

1 About $x=0$ with $\omega=\sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$
2 About $x=0$ with $\omega=\sqrt{\frac{m}{k}}$
3 About $\mathrm{x}=\frac{\mathrm{F}_{0}}{\mathrm{k}}$ with $\omega=\sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$
4 About $\mathrm{x}=\frac{\mathrm{F}_{0}}{\mathrm{k}}$ with $\omega \neq \sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$
Oscillations

140807 A small block of mass $100 \mathrm{~g}$ is tied to a spring of spring constant $7.5 \mathrm{~N} / \mathrm{m}$ and length $20 \mathrm{~cm}$. the other end of spring is fixed at a particular point $A$. If the block moves in a circular path on a smooth horizontal surface with constant angular velocity $5 \mathrm{rad} / \mathrm{s}$ about point $A$, then tension in the spring is

1 $1.5 \mathrm{~N}$
2 $0.75 \mathrm{~N}$
3 $0.25 \mathrm{~N}$
4 $0.50 \mathrm{~N}$
Oscillations

140808 If the amplitude of a lightly damped oscillator decreases by $1.5 \%$ then the mechanical energy of the oscillator lost in each cycle is

1 $1.5 \%$
2 $0.75 \%$
3 $6 \%$
4 $3 \%$
Oscillations

140809 The amplitude of a damped oscillator varies with time as $A(t)=A_{0} \exp (-b t / 2 m)$ where $b=$ $70 \mathrm{~g} / \mathrm{s}$ and $\mathrm{m}=200 \mathrm{~g}$. How long does it take for the mechanical energy to drop to one - fourth of its initial value?
[Take $\ln 2=0.7]$

1 $2.0 \mathrm{~s}$
2 $4.0 \mathrm{~s}$
3 $2.5 \mathrm{~s}$
4 $3.5 \mathrm{~s}$
Oscillations

140810 The amplitude of a damped oscillator is known to decreases to 0.9 times its original magnitude in 5 seconds. Approximately, by how many times its original magnitude will its amplitude decrease after another 10 seconds?

1 0.73
2 0.9
3 0.59
4 0.26
Oscillations

140811 A particle of mass ' $m$ ' is under an influence of a force $\overrightarrow{\mathbf{F}}=-\mathbf{k} \overrightarrow{\mathbf{x}}+\overrightarrow{\mathbf{F}}_{0}$. The particle when disturbed will oscillate

1 About $x=0$ with $\omega=\sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$
2 About $x=0$ with $\omega=\sqrt{\frac{m}{k}}$
3 About $\mathrm{x}=\frac{\mathrm{F}_{0}}{\mathrm{k}}$ with $\omega=\sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$
4 About $\mathrm{x}=\frac{\mathrm{F}_{0}}{\mathrm{k}}$ with $\omega \neq \sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$
Oscillations

140807 A small block of mass $100 \mathrm{~g}$ is tied to a spring of spring constant $7.5 \mathrm{~N} / \mathrm{m}$ and length $20 \mathrm{~cm}$. the other end of spring is fixed at a particular point $A$. If the block moves in a circular path on a smooth horizontal surface with constant angular velocity $5 \mathrm{rad} / \mathrm{s}$ about point $A$, then tension in the spring is

1 $1.5 \mathrm{~N}$
2 $0.75 \mathrm{~N}$
3 $0.25 \mathrm{~N}$
4 $0.50 \mathrm{~N}$
Oscillations

140808 If the amplitude of a lightly damped oscillator decreases by $1.5 \%$ then the mechanical energy of the oscillator lost in each cycle is

1 $1.5 \%$
2 $0.75 \%$
3 $6 \%$
4 $3 \%$
Oscillations

140809 The amplitude of a damped oscillator varies with time as $A(t)=A_{0} \exp (-b t / 2 m)$ where $b=$ $70 \mathrm{~g} / \mathrm{s}$ and $\mathrm{m}=200 \mathrm{~g}$. How long does it take for the mechanical energy to drop to one - fourth of its initial value?
[Take $\ln 2=0.7]$

1 $2.0 \mathrm{~s}$
2 $4.0 \mathrm{~s}$
3 $2.5 \mathrm{~s}$
4 $3.5 \mathrm{~s}$
Oscillations

140810 The amplitude of a damped oscillator is known to decreases to 0.9 times its original magnitude in 5 seconds. Approximately, by how many times its original magnitude will its amplitude decrease after another 10 seconds?

1 0.73
2 0.9
3 0.59
4 0.26
Oscillations

140811 A particle of mass ' $m$ ' is under an influence of a force $\overrightarrow{\mathbf{F}}=-\mathbf{k} \overrightarrow{\mathbf{x}}+\overrightarrow{\mathbf{F}}_{0}$. The particle when disturbed will oscillate

1 About $x=0$ with $\omega=\sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$
2 About $x=0$ with $\omega=\sqrt{\frac{m}{k}}$
3 About $\mathrm{x}=\frac{\mathrm{F}_{0}}{\mathrm{k}}$ with $\omega=\sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$
4 About $\mathrm{x}=\frac{\mathrm{F}_{0}}{\mathrm{k}}$ with $\omega \neq \sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$
Oscillations

140807 A small block of mass $100 \mathrm{~g}$ is tied to a spring of spring constant $7.5 \mathrm{~N} / \mathrm{m}$ and length $20 \mathrm{~cm}$. the other end of spring is fixed at a particular point $A$. If the block moves in a circular path on a smooth horizontal surface with constant angular velocity $5 \mathrm{rad} / \mathrm{s}$ about point $A$, then tension in the spring is

1 $1.5 \mathrm{~N}$
2 $0.75 \mathrm{~N}$
3 $0.25 \mathrm{~N}$
4 $0.50 \mathrm{~N}$
Oscillations

140808 If the amplitude of a lightly damped oscillator decreases by $1.5 \%$ then the mechanical energy of the oscillator lost in each cycle is

1 $1.5 \%$
2 $0.75 \%$
3 $6 \%$
4 $3 \%$
Oscillations

140809 The amplitude of a damped oscillator varies with time as $A(t)=A_{0} \exp (-b t / 2 m)$ where $b=$ $70 \mathrm{~g} / \mathrm{s}$ and $\mathrm{m}=200 \mathrm{~g}$. How long does it take for the mechanical energy to drop to one - fourth of its initial value?
[Take $\ln 2=0.7]$

1 $2.0 \mathrm{~s}$
2 $4.0 \mathrm{~s}$
3 $2.5 \mathrm{~s}$
4 $3.5 \mathrm{~s}$
Oscillations

140810 The amplitude of a damped oscillator is known to decreases to 0.9 times its original magnitude in 5 seconds. Approximately, by how many times its original magnitude will its amplitude decrease after another 10 seconds?

1 0.73
2 0.9
3 0.59
4 0.26
Oscillations

140811 A particle of mass ' $m$ ' is under an influence of a force $\overrightarrow{\mathbf{F}}=-\mathbf{k} \overrightarrow{\mathbf{x}}+\overrightarrow{\mathbf{F}}_{0}$. The particle when disturbed will oscillate

1 About $x=0$ with $\omega=\sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$
2 About $x=0$ with $\omega=\sqrt{\frac{m}{k}}$
3 About $\mathrm{x}=\frac{\mathrm{F}_{0}}{\mathrm{k}}$ with $\omega=\sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$
4 About $\mathrm{x}=\frac{\mathrm{F}_{0}}{\mathrm{k}}$ with $\omega \neq \sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$