Damped Simple Harmonic Motion
PHXI14:OSCILLATIONS

364228 Two simple harmonic motions are represented by the equations \(y_{1}=0.1 \sin \left(100 \pi t+\dfrac{\pi}{3}\right)\) and \(y_{1}=0.1 \cos \pi t\). The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is

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

364229 Two particles are executing simple harmonic motion of the same amplitude \(A\) and frequency \(\omega\) along the \(x\)-axis. Their mean position is separated by distance \(X_{0}\left(X_{0}>A\right)\). If the maximum separation between them is \(A\), the phase difference between thier motion is:

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

364230 In SHM phase difference between displacement and velocity is \(\phi_{1}\) and that between displacement and acceleration is \(\phi_{2}\), then

1 \({\phi _2} = 2{\phi _1}\)
2 \(\phi_{2}=\phi_{1}\)
3 \(\phi_{1}=2 \phi_{2}\)
4 None of these
PHXI14:OSCILLATIONS

364231 Two simple pendulum of length \(1\;m\) and \(4\;m\) respectively are given small linear displacement in one direction at the same time. They will again be in the phase when the pendulum of shorter length has completed oscillations \(\left[n T_{1}=(n-1) T_{2}\right.\), where \(T_{1}\) is time period of shorter length \({T_2}\) be time period of longer wavelength and \(n\) are no. of oscillations completed]

1 2
2 5
3 3
4 4
PHXI14:OSCILLATIONS

364228 Two simple harmonic motions are represented by the equations \(y_{1}=0.1 \sin \left(100 \pi t+\dfrac{\pi}{3}\right)\) and \(y_{1}=0.1 \cos \pi t\). The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is

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

364229 Two particles are executing simple harmonic motion of the same amplitude \(A\) and frequency \(\omega\) along the \(x\)-axis. Their mean position is separated by distance \(X_{0}\left(X_{0}>A\right)\). If the maximum separation between them is \(A\), the phase difference between thier motion is:

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

364230 In SHM phase difference between displacement and velocity is \(\phi_{1}\) and that between displacement and acceleration is \(\phi_{2}\), then

1 \({\phi _2} = 2{\phi _1}\)
2 \(\phi_{2}=\phi_{1}\)
3 \(\phi_{1}=2 \phi_{2}\)
4 None of these
PHXI14:OSCILLATIONS

364231 Two simple pendulum of length \(1\;m\) and \(4\;m\) respectively are given small linear displacement in one direction at the same time. They will again be in the phase when the pendulum of shorter length has completed oscillations \(\left[n T_{1}=(n-1) T_{2}\right.\), where \(T_{1}\) is time period of shorter length \({T_2}\) be time period of longer wavelength and \(n\) are no. of oscillations completed]

1 2
2 5
3 3
4 4
PHXI14:OSCILLATIONS

364228 Two simple harmonic motions are represented by the equations \(y_{1}=0.1 \sin \left(100 \pi t+\dfrac{\pi}{3}\right)\) and \(y_{1}=0.1 \cos \pi t\). The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is

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

364229 Two particles are executing simple harmonic motion of the same amplitude \(A\) and frequency \(\omega\) along the \(x\)-axis. Their mean position is separated by distance \(X_{0}\left(X_{0}>A\right)\). If the maximum separation between them is \(A\), the phase difference between thier motion is:

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

364230 In SHM phase difference between displacement and velocity is \(\phi_{1}\) and that between displacement and acceleration is \(\phi_{2}\), then

1 \({\phi _2} = 2{\phi _1}\)
2 \(\phi_{2}=\phi_{1}\)
3 \(\phi_{1}=2 \phi_{2}\)
4 None of these
PHXI14:OSCILLATIONS

364231 Two simple pendulum of length \(1\;m\) and \(4\;m\) respectively are given small linear displacement in one direction at the same time. They will again be in the phase when the pendulum of shorter length has completed oscillations \(\left[n T_{1}=(n-1) T_{2}\right.\), where \(T_{1}\) is time period of shorter length \({T_2}\) be time period of longer wavelength and \(n\) are no. of oscillations completed]

1 2
2 5
3 3
4 4
PHXI14:OSCILLATIONS

364228 Two simple harmonic motions are represented by the equations \(y_{1}=0.1 \sin \left(100 \pi t+\dfrac{\pi}{3}\right)\) and \(y_{1}=0.1 \cos \pi t\). The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is

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

364229 Two particles are executing simple harmonic motion of the same amplitude \(A\) and frequency \(\omega\) along the \(x\)-axis. Their mean position is separated by distance \(X_{0}\left(X_{0}>A\right)\). If the maximum separation between them is \(A\), the phase difference between thier motion is:

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

364230 In SHM phase difference between displacement and velocity is \(\phi_{1}\) and that between displacement and acceleration is \(\phi_{2}\), then

1 \({\phi _2} = 2{\phi _1}\)
2 \(\phi_{2}=\phi_{1}\)
3 \(\phi_{1}=2 \phi_{2}\)
4 None of these
PHXI14:OSCILLATIONS

364231 Two simple pendulum of length \(1\;m\) and \(4\;m\) respectively are given small linear displacement in one direction at the same time. They will again be in the phase when the pendulum of shorter length has completed oscillations \(\left[n T_{1}=(n-1) T_{2}\right.\), where \(T_{1}\) is time period of shorter length \({T_2}\) be time period of longer wavelength and \(n\) are no. of oscillations completed]

1 2
2 5
3 3
4 4