Damped Simple Harmonic Motion
PHXI14:OSCILLATIONS

364223 Two particles are executing simple harmonic motion. At an instant of time \(t\) their displacements are \({y_1} = a\cos (\omega t)\) and \({y_2} = a\sin (\omega t)\). Then the phase difference between \({y_1}\) and \({y_2}\) is

1 \(120^{\circ}\)
2 \(90^{\circ}\)
3 \(180^{\circ}\)
4 zero
PHXI14:OSCILLATIONS

364224 Two pendulums start oscillating in the same direction at the same time from the same mean position. Their time periods are respectively \(2\;s\) and \(1.5\;s\). The phase difference betwen them, when the smaller pendulum has completed one vibration, will be

1 \(\pi / 2\)
2 \(\pi / 4\)
3 \(3 \pi / 2\)
4 \(2\,\pi /3\)
PHXI14:OSCILLATIONS

364225 The phase difference between two particles executing SHM of the same amplitudes and frequency along same straight line while passing one another when going in opposite directions with equal displacement from their respective starting point is \(2\,\pi /3\). If the phase of one particle is \(\pi / 6\), find the displacement at this instant, if amplitude is \(A\).

1 \(2\;A/3\)
2 \(A/3\)
3 \(A/2\)
4 \(3\;A/4\)
PHXI14:OSCILLATIONS

364226 Two simple harmonic motions are represented by equations
\(y_{1}=4 \sin (10 t+\phi)\) and \(y_{2}=5 \cos 10 t\). What is the phase difference between their velocities?

1 \(-\phi\)
2 \(\phi\)
3 \(\left(\phi-\dfrac{\pi}{2}\right)\)
4 \(\left(\phi+\dfrac{\pi}{2}\right)\)
PHXI14:OSCILLATIONS

364227 What is the phase difference between two simple harmonic motions represented by
\(X_{1}=A \sin \left[\omega t+\dfrac{\pi}{6}\right] \text { and } X_{2}=A \cos \omega t ?\)

1 \(\dfrac{\pi}{6}\)
2 \(\dfrac{\pi}{3}\)
3 \(\dfrac{\pi}{2}\)
4 \(\dfrac{2 \pi}{3}\)
PHXI14:OSCILLATIONS

364223 Two particles are executing simple harmonic motion. At an instant of time \(t\) their displacements are \({y_1} = a\cos (\omega t)\) and \({y_2} = a\sin (\omega t)\). Then the phase difference between \({y_1}\) and \({y_2}\) is

1 \(120^{\circ}\)
2 \(90^{\circ}\)
3 \(180^{\circ}\)
4 zero
PHXI14:OSCILLATIONS

364224 Two pendulums start oscillating in the same direction at the same time from the same mean position. Their time periods are respectively \(2\;s\) and \(1.5\;s\). The phase difference betwen them, when the smaller pendulum has completed one vibration, will be

1 \(\pi / 2\)
2 \(\pi / 4\)
3 \(3 \pi / 2\)
4 \(2\,\pi /3\)
PHXI14:OSCILLATIONS

364225 The phase difference between two particles executing SHM of the same amplitudes and frequency along same straight line while passing one another when going in opposite directions with equal displacement from their respective starting point is \(2\,\pi /3\). If the phase of one particle is \(\pi / 6\), find the displacement at this instant, if amplitude is \(A\).

1 \(2\;A/3\)
2 \(A/3\)
3 \(A/2\)
4 \(3\;A/4\)
PHXI14:OSCILLATIONS

364226 Two simple harmonic motions are represented by equations
\(y_{1}=4 \sin (10 t+\phi)\) and \(y_{2}=5 \cos 10 t\). What is the phase difference between their velocities?

1 \(-\phi\)
2 \(\phi\)
3 \(\left(\phi-\dfrac{\pi}{2}\right)\)
4 \(\left(\phi+\dfrac{\pi}{2}\right)\)
PHXI14:OSCILLATIONS

364227 What is the phase difference between two simple harmonic motions represented by
\(X_{1}=A \sin \left[\omega t+\dfrac{\pi}{6}\right] \text { and } X_{2}=A \cos \omega t ?\)

1 \(\dfrac{\pi}{6}\)
2 \(\dfrac{\pi}{3}\)
3 \(\dfrac{\pi}{2}\)
4 \(\dfrac{2 \pi}{3}\)
PHXI14:OSCILLATIONS

364223 Two particles are executing simple harmonic motion. At an instant of time \(t\) their displacements are \({y_1} = a\cos (\omega t)\) and \({y_2} = a\sin (\omega t)\). Then the phase difference between \({y_1}\) and \({y_2}\) is

1 \(120^{\circ}\)
2 \(90^{\circ}\)
3 \(180^{\circ}\)
4 zero
PHXI14:OSCILLATIONS

364224 Two pendulums start oscillating in the same direction at the same time from the same mean position. Their time periods are respectively \(2\;s\) and \(1.5\;s\). The phase difference betwen them, when the smaller pendulum has completed one vibration, will be

1 \(\pi / 2\)
2 \(\pi / 4\)
3 \(3 \pi / 2\)
4 \(2\,\pi /3\)
PHXI14:OSCILLATIONS

364225 The phase difference between two particles executing SHM of the same amplitudes and frequency along same straight line while passing one another when going in opposite directions with equal displacement from their respective starting point is \(2\,\pi /3\). If the phase of one particle is \(\pi / 6\), find the displacement at this instant, if amplitude is \(A\).

1 \(2\;A/3\)
2 \(A/3\)
3 \(A/2\)
4 \(3\;A/4\)
PHXI14:OSCILLATIONS

364226 Two simple harmonic motions are represented by equations
\(y_{1}=4 \sin (10 t+\phi)\) and \(y_{2}=5 \cos 10 t\). What is the phase difference between their velocities?

1 \(-\phi\)
2 \(\phi\)
3 \(\left(\phi-\dfrac{\pi}{2}\right)\)
4 \(\left(\phi+\dfrac{\pi}{2}\right)\)
PHXI14:OSCILLATIONS

364227 What is the phase difference between two simple harmonic motions represented by
\(X_{1}=A \sin \left[\omega t+\dfrac{\pi}{6}\right] \text { and } X_{2}=A \cos \omega t ?\)

1 \(\dfrac{\pi}{6}\)
2 \(\dfrac{\pi}{3}\)
3 \(\dfrac{\pi}{2}\)
4 \(\dfrac{2 \pi}{3}\)
PHXI14:OSCILLATIONS

364223 Two particles are executing simple harmonic motion. At an instant of time \(t\) their displacements are \({y_1} = a\cos (\omega t)\) and \({y_2} = a\sin (\omega t)\). Then the phase difference between \({y_1}\) and \({y_2}\) is

1 \(120^{\circ}\)
2 \(90^{\circ}\)
3 \(180^{\circ}\)
4 zero
PHXI14:OSCILLATIONS

364224 Two pendulums start oscillating in the same direction at the same time from the same mean position. Their time periods are respectively \(2\;s\) and \(1.5\;s\). The phase difference betwen them, when the smaller pendulum has completed one vibration, will be

1 \(\pi / 2\)
2 \(\pi / 4\)
3 \(3 \pi / 2\)
4 \(2\,\pi /3\)
PHXI14:OSCILLATIONS

364225 The phase difference between two particles executing SHM of the same amplitudes and frequency along same straight line while passing one another when going in opposite directions with equal displacement from their respective starting point is \(2\,\pi /3\). If the phase of one particle is \(\pi / 6\), find the displacement at this instant, if amplitude is \(A\).

1 \(2\;A/3\)
2 \(A/3\)
3 \(A/2\)
4 \(3\;A/4\)
PHXI14:OSCILLATIONS

364226 Two simple harmonic motions are represented by equations
\(y_{1}=4 \sin (10 t+\phi)\) and \(y_{2}=5 \cos 10 t\). What is the phase difference between their velocities?

1 \(-\phi\)
2 \(\phi\)
3 \(\left(\phi-\dfrac{\pi}{2}\right)\)
4 \(\left(\phi+\dfrac{\pi}{2}\right)\)
PHXI14:OSCILLATIONS

364227 What is the phase difference between two simple harmonic motions represented by
\(X_{1}=A \sin \left[\omega t+\dfrac{\pi}{6}\right] \text { and } X_{2}=A \cos \omega t ?\)

1 \(\dfrac{\pi}{6}\)
2 \(\dfrac{\pi}{3}\)
3 \(\dfrac{\pi}{2}\)
4 \(\dfrac{2 \pi}{3}\)
PHXI14:OSCILLATIONS

364223 Two particles are executing simple harmonic motion. At an instant of time \(t\) their displacements are \({y_1} = a\cos (\omega t)\) and \({y_2} = a\sin (\omega t)\). Then the phase difference between \({y_1}\) and \({y_2}\) is

1 \(120^{\circ}\)
2 \(90^{\circ}\)
3 \(180^{\circ}\)
4 zero
PHXI14:OSCILLATIONS

364224 Two pendulums start oscillating in the same direction at the same time from the same mean position. Their time periods are respectively \(2\;s\) and \(1.5\;s\). The phase difference betwen them, when the smaller pendulum has completed one vibration, will be

1 \(\pi / 2\)
2 \(\pi / 4\)
3 \(3 \pi / 2\)
4 \(2\,\pi /3\)
PHXI14:OSCILLATIONS

364225 The phase difference between two particles executing SHM of the same amplitudes and frequency along same straight line while passing one another when going in opposite directions with equal displacement from their respective starting point is \(2\,\pi /3\). If the phase of one particle is \(\pi / 6\), find the displacement at this instant, if amplitude is \(A\).

1 \(2\;A/3\)
2 \(A/3\)
3 \(A/2\)
4 \(3\;A/4\)
PHXI14:OSCILLATIONS

364226 Two simple harmonic motions are represented by equations
\(y_{1}=4 \sin (10 t+\phi)\) and \(y_{2}=5 \cos 10 t\). What is the phase difference between their velocities?

1 \(-\phi\)
2 \(\phi\)
3 \(\left(\phi-\dfrac{\pi}{2}\right)\)
4 \(\left(\phi+\dfrac{\pi}{2}\right)\)
PHXI14:OSCILLATIONS

364227 What is the phase difference between two simple harmonic motions represented by
\(X_{1}=A \sin \left[\omega t+\dfrac{\pi}{6}\right] \text { and } X_{2}=A \cos \omega t ?\)

1 \(\dfrac{\pi}{6}\)
2 \(\dfrac{\pi}{3}\)
3 \(\dfrac{\pi}{2}\)
4 \(\dfrac{2 \pi}{3}\)