Damped Simple Harmonic Motion
PHXI14:OSCILLATIONS

364236 An object of mass \(m\) is moving in a uniform circular motion in the \(xy\) plane. The circle has radius \(R\) and the object is moving around the circle with speed \(v\). The motion is projected onto the \(x\)-axis where it appears as simple harmonic motion according to \(x(t) = R\cos (\omega t + \phi )\). Here \(\omega\) is equal to

1 \(v / R\)
2 \(v /(R \sin \omega t)\)
3 \({m^2}R\)
4 \(\mathrm{R} / v\)
PHXI14:OSCILLATIONS

364237 A stone is swinging in a horizontal circle \(0.8\;m\) in diameter, at \(30\,rev/\min \). A distant light causes a shadow of the stone to be formed on a nearby wall. What is the amplitude of the motion of the shadow? what is the frequency?

1 \(0.4\;m,1.5\;Hz\)
2 \(0.4\;m,0.5\;Hz\)
3 \(0.8\;m,0.5\;Hz\)
4 \(0.2\;m,0.5\;Hz\)
PHXI14:OSCILLATIONS

364238 The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the fig.
\(y\) - projection of the radius vector of rotating particle \(P\) is
supporting img

1 \(y(t)=-3 \cos 2 \pi t\), where \(y\) in \(m\)
2 \(y(t)=4 \sin \left(\dfrac{\pi t}{2}\right)\), where \(y\) in \(m\)
3 \(y(t)=3 \cos \left(\dfrac{3 \pi t}{2}\right)\), where \(y\) in \(m\)
4 \(y(t)=3 \cos \left(\dfrac{\pi t}{2}\right)\), where \(y\) in \(m\)
PHXI14:OSCILLATIONS

364239 Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the \(x\)-projection of the radius vetor of the rotating particle \(P\) is
supporting img

1 \(x(t)=B \cos \left(\dfrac{\pi t}{15}\right)\)
2 \(x(t)=B \sin \left(\dfrac{2 \pi t}{30}\right)\)
3 \(x(t)=B\left(\dfrac{\pi t}{15}+\dfrac{\pi}{2}\right)\)
4 \(x(t)=B \sin \left(\dfrac{\pi t}{15}+\dfrac{\pi}{2}\right)\)
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
PHXI14:OSCILLATIONS

364236 An object of mass \(m\) is moving in a uniform circular motion in the \(xy\) plane. The circle has radius \(R\) and the object is moving around the circle with speed \(v\). The motion is projected onto the \(x\)-axis where it appears as simple harmonic motion according to \(x(t) = R\cos (\omega t + \phi )\). Here \(\omega\) is equal to

1 \(v / R\)
2 \(v /(R \sin \omega t)\)
3 \({m^2}R\)
4 \(\mathrm{R} / v\)
PHXI14:OSCILLATIONS

364237 A stone is swinging in a horizontal circle \(0.8\;m\) in diameter, at \(30\,rev/\min \). A distant light causes a shadow of the stone to be formed on a nearby wall. What is the amplitude of the motion of the shadow? what is the frequency?

1 \(0.4\;m,1.5\;Hz\)
2 \(0.4\;m,0.5\;Hz\)
3 \(0.8\;m,0.5\;Hz\)
4 \(0.2\;m,0.5\;Hz\)
PHXI14:OSCILLATIONS

364238 The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the fig.
\(y\) - projection of the radius vector of rotating particle \(P\) is
supporting img

1 \(y(t)=-3 \cos 2 \pi t\), where \(y\) in \(m\)
2 \(y(t)=4 \sin \left(\dfrac{\pi t}{2}\right)\), where \(y\) in \(m\)
3 \(y(t)=3 \cos \left(\dfrac{3 \pi t}{2}\right)\), where \(y\) in \(m\)
4 \(y(t)=3 \cos \left(\dfrac{\pi t}{2}\right)\), where \(y\) in \(m\)
PHXI14:OSCILLATIONS

364239 Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the \(x\)-projection of the radius vetor of the rotating particle \(P\) is
supporting img

1 \(x(t)=B \cos \left(\dfrac{\pi t}{15}\right)\)
2 \(x(t)=B \sin \left(\dfrac{2 \pi t}{30}\right)\)
3 \(x(t)=B\left(\dfrac{\pi t}{15}+\dfrac{\pi}{2}\right)\)
4 \(x(t)=B \sin \left(\dfrac{\pi t}{15}+\dfrac{\pi}{2}\right)\)
PHXI14:OSCILLATIONS

364236 An object of mass \(m\) is moving in a uniform circular motion in the \(xy\) plane. The circle has radius \(R\) and the object is moving around the circle with speed \(v\). The motion is projected onto the \(x\)-axis where it appears as simple harmonic motion according to \(x(t) = R\cos (\omega t + \phi )\). Here \(\omega\) is equal to

1 \(v / R\)
2 \(v /(R \sin \omega t)\)
3 \({m^2}R\)
4 \(\mathrm{R} / v\)
PHXI14:OSCILLATIONS

364237 A stone is swinging in a horizontal circle \(0.8\;m\) in diameter, at \(30\,rev/\min \). A distant light causes a shadow of the stone to be formed on a nearby wall. What is the amplitude of the motion of the shadow? what is the frequency?

1 \(0.4\;m,1.5\;Hz\)
2 \(0.4\;m,0.5\;Hz\)
3 \(0.8\;m,0.5\;Hz\)
4 \(0.2\;m,0.5\;Hz\)
PHXI14:OSCILLATIONS

364238 The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the fig.
\(y\) - projection of the radius vector of rotating particle \(P\) is
supporting img

1 \(y(t)=-3 \cos 2 \pi t\), where \(y\) in \(m\)
2 \(y(t)=4 \sin \left(\dfrac{\pi t}{2}\right)\), where \(y\) in \(m\)
3 \(y(t)=3 \cos \left(\dfrac{3 \pi t}{2}\right)\), where \(y\) in \(m\)
4 \(y(t)=3 \cos \left(\dfrac{\pi t}{2}\right)\), where \(y\) in \(m\)
PHXI14:OSCILLATIONS

364239 Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the \(x\)-projection of the radius vetor of the rotating particle \(P\) is
supporting img

1 \(x(t)=B \cos \left(\dfrac{\pi t}{15}\right)\)
2 \(x(t)=B \sin \left(\dfrac{2 \pi t}{30}\right)\)
3 \(x(t)=B\left(\dfrac{\pi t}{15}+\dfrac{\pi}{2}\right)\)
4 \(x(t)=B \sin \left(\dfrac{\pi t}{15}+\dfrac{\pi}{2}\right)\)
PHXI14:OSCILLATIONS

364236 An object of mass \(m\) is moving in a uniform circular motion in the \(xy\) plane. The circle has radius \(R\) and the object is moving around the circle with speed \(v\). The motion is projected onto the \(x\)-axis where it appears as simple harmonic motion according to \(x(t) = R\cos (\omega t + \phi )\). Here \(\omega\) is equal to

1 \(v / R\)
2 \(v /(R \sin \omega t)\)
3 \({m^2}R\)
4 \(\mathrm{R} / v\)
PHXI14:OSCILLATIONS

364237 A stone is swinging in a horizontal circle \(0.8\;m\) in diameter, at \(30\,rev/\min \). A distant light causes a shadow of the stone to be formed on a nearby wall. What is the amplitude of the motion of the shadow? what is the frequency?

1 \(0.4\;m,1.5\;Hz\)
2 \(0.4\;m,0.5\;Hz\)
3 \(0.8\;m,0.5\;Hz\)
4 \(0.2\;m,0.5\;Hz\)
PHXI14:OSCILLATIONS

364238 The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the fig.
\(y\) - projection of the radius vector of rotating particle \(P\) is
supporting img

1 \(y(t)=-3 \cos 2 \pi t\), where \(y\) in \(m\)
2 \(y(t)=4 \sin \left(\dfrac{\pi t}{2}\right)\), where \(y\) in \(m\)
3 \(y(t)=3 \cos \left(\dfrac{3 \pi t}{2}\right)\), where \(y\) in \(m\)
4 \(y(t)=3 \cos \left(\dfrac{\pi t}{2}\right)\), where \(y\) in \(m\)
PHXI14:OSCILLATIONS

364239 Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the \(x\)-projection of the radius vetor of the rotating particle \(P\) is
supporting img

1 \(x(t)=B \cos \left(\dfrac{\pi t}{15}\right)\)
2 \(x(t)=B \sin \left(\dfrac{2 \pi t}{30}\right)\)
3 \(x(t)=B\left(\dfrac{\pi t}{15}+\dfrac{\pi}{2}\right)\)
4 \(x(t)=B \sin \left(\dfrac{\pi t}{15}+\dfrac{\pi}{2}\right)\)