Some Systems Executing Simple Harmonic Motion
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PHXI14:OSCILLATIONS

364368 The pulley shown in the figure. has a radius \(r\), moment of inertia \(I\) about its axis and mass \(m\). Find the time period of vertical oscillations of its centre of mass. the spring constant of spring is \(K\) and the spring does not slip over the pulley.
supporting img

1 \(\pi \sqrt{\dfrac{m+I / R^{2}}{K}}\)
2 \(2 \pi \sqrt{\dfrac{m+I / R^{2}}{2 K}}\)
3 \(2 \pi \sqrt{\dfrac{2 m+I / R^{2}}{K}}\)
4 \(2 \pi \sqrt{\dfrac{m+I / R^{2}}{K}}\)
PHXI14:OSCILLATIONS

364369 Two identical springs of spring constant \(k\) each are connected in series and parallel as shown in figure. A mass \(M\) is suspended from them. The ratio of their frequencies of vertical oscillation will be
supporting img

1 \(1: 2\)
2 \(2: 1\)
3 \(4: 1\)
4 \(1: 4\)
PHXI14:OSCILLATIONS

364370 A body of mass \(m\) hangs from a smooth light fixed pulley \(P_{1}\) by the inextensible string fitted with the springs of stiffness \(k_{1}\) and \(k_{2}\). the string passes over the smooth light pulley \(P_{2}\) which is connected with another ideal spring of stiffness \(k_{2}\). Find the period of oscillation of the body.
supporting img

1 \(2 \pi \sqrt{m\left(\dfrac{1}{K_{1}}+\dfrac{4}{K_{2}}+\dfrac{1}{K_{3}}\right)}\)
2 \(2 \pi \sqrt{m\left(\dfrac{1}{K_{1}}+\dfrac{2}{K_{2}}+\dfrac{1}{K_{3}}\right)}\)
3 \({\rm{ }}2\pi \sqrt {m\left( {\frac{1}{{{K_1}}} + \frac{1}{{{K_2}}} + \frac{1}{{{K_3}}}} \right)} \)
4 \(2\pi \sqrt {m\left( {\frac{2}{{{K_1}}} + \frac{1}{{{K_2}}} + \frac{2}{{{K_3}}}} \right)} \)
PHXI14:OSCILLATIONS

364371 supporting img

1 A - P, B - Q, C - S, D - R
2 A - S, B - R, C - P, D - Q
3 A - R, B - P, C - S, D - Q
4 A - P, B - R, C - Q, D - S
PHXI14:OSCILLATIONS

364372 Two springs, of force constants \(k_{1}\) and \(k_{2}\) are connected to a mass \(m\) as shown. The frequency of oscillation of the mass is \(f\). If both \(k_{1}\) and \(k_{2}\) are made four times their original values, the frequency of oscillation becomes.
supporting img

1 \(2 f\)
2 \(f / 2\)
3 \(f / 4\)
4 \(4 f\)
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PHXI14:OSCILLATIONS

364368 The pulley shown in the figure. has a radius \(r\), moment of inertia \(I\) about its axis and mass \(m\). Find the time period of vertical oscillations of its centre of mass. the spring constant of spring is \(K\) and the spring does not slip over the pulley.
supporting img

1 \(\pi \sqrt{\dfrac{m+I / R^{2}}{K}}\)
2 \(2 \pi \sqrt{\dfrac{m+I / R^{2}}{2 K}}\)
3 \(2 \pi \sqrt{\dfrac{2 m+I / R^{2}}{K}}\)
4 \(2 \pi \sqrt{\dfrac{m+I / R^{2}}{K}}\)
PHXI14:OSCILLATIONS

364369 Two identical springs of spring constant \(k\) each are connected in series and parallel as shown in figure. A mass \(M\) is suspended from them. The ratio of their frequencies of vertical oscillation will be
supporting img

1 \(1: 2\)
2 \(2: 1\)
3 \(4: 1\)
4 \(1: 4\)
PHXI14:OSCILLATIONS

364370 A body of mass \(m\) hangs from a smooth light fixed pulley \(P_{1}\) by the inextensible string fitted with the springs of stiffness \(k_{1}\) and \(k_{2}\). the string passes over the smooth light pulley \(P_{2}\) which is connected with another ideal spring of stiffness \(k_{2}\). Find the period of oscillation of the body.
supporting img

1 \(2 \pi \sqrt{m\left(\dfrac{1}{K_{1}}+\dfrac{4}{K_{2}}+\dfrac{1}{K_{3}}\right)}\)
2 \(2 \pi \sqrt{m\left(\dfrac{1}{K_{1}}+\dfrac{2}{K_{2}}+\dfrac{1}{K_{3}}\right)}\)
3 \({\rm{ }}2\pi \sqrt {m\left( {\frac{1}{{{K_1}}} + \frac{1}{{{K_2}}} + \frac{1}{{{K_3}}}} \right)} \)
4 \(2\pi \sqrt {m\left( {\frac{2}{{{K_1}}} + \frac{1}{{{K_2}}} + \frac{2}{{{K_3}}}} \right)} \)
PHXI14:OSCILLATIONS

364371 supporting img

1 A - P, B - Q, C - S, D - R
2 A - S, B - R, C - P, D - Q
3 A - R, B - P, C - S, D - Q
4 A - P, B - R, C - Q, D - S
PHXI14:OSCILLATIONS

364372 Two springs, of force constants \(k_{1}\) and \(k_{2}\) are connected to a mass \(m\) as shown. The frequency of oscillation of the mass is \(f\). If both \(k_{1}\) and \(k_{2}\) are made four times their original values, the frequency of oscillation becomes.
supporting img

1 \(2 f\)
2 \(f / 2\)
3 \(f / 4\)
4 \(4 f\)
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PHXI14:OSCILLATIONS

364368 The pulley shown in the figure. has a radius \(r\), moment of inertia \(I\) about its axis and mass \(m\). Find the time period of vertical oscillations of its centre of mass. the spring constant of spring is \(K\) and the spring does not slip over the pulley.
supporting img

1 \(\pi \sqrt{\dfrac{m+I / R^{2}}{K}}\)
2 \(2 \pi \sqrt{\dfrac{m+I / R^{2}}{2 K}}\)
3 \(2 \pi \sqrt{\dfrac{2 m+I / R^{2}}{K}}\)
4 \(2 \pi \sqrt{\dfrac{m+I / R^{2}}{K}}\)
PHXI14:OSCILLATIONS

364369 Two identical springs of spring constant \(k\) each are connected in series and parallel as shown in figure. A mass \(M\) is suspended from them. The ratio of their frequencies of vertical oscillation will be
supporting img

1 \(1: 2\)
2 \(2: 1\)
3 \(4: 1\)
4 \(1: 4\)
PHXI14:OSCILLATIONS

364370 A body of mass \(m\) hangs from a smooth light fixed pulley \(P_{1}\) by the inextensible string fitted with the springs of stiffness \(k_{1}\) and \(k_{2}\). the string passes over the smooth light pulley \(P_{2}\) which is connected with another ideal spring of stiffness \(k_{2}\). Find the period of oscillation of the body.
supporting img

1 \(2 \pi \sqrt{m\left(\dfrac{1}{K_{1}}+\dfrac{4}{K_{2}}+\dfrac{1}{K_{3}}\right)}\)
2 \(2 \pi \sqrt{m\left(\dfrac{1}{K_{1}}+\dfrac{2}{K_{2}}+\dfrac{1}{K_{3}}\right)}\)
3 \({\rm{ }}2\pi \sqrt {m\left( {\frac{1}{{{K_1}}} + \frac{1}{{{K_2}}} + \frac{1}{{{K_3}}}} \right)} \)
4 \(2\pi \sqrt {m\left( {\frac{2}{{{K_1}}} + \frac{1}{{{K_2}}} + \frac{2}{{{K_3}}}} \right)} \)
PHXI14:OSCILLATIONS

364371 supporting img

1 A - P, B - Q, C - S, D - R
2 A - S, B - R, C - P, D - Q
3 A - R, B - P, C - S, D - Q
4 A - P, B - R, C - Q, D - S
PHXI14:OSCILLATIONS

364372 Two springs, of force constants \(k_{1}\) and \(k_{2}\) are connected to a mass \(m\) as shown. The frequency of oscillation of the mass is \(f\). If both \(k_{1}\) and \(k_{2}\) are made four times their original values, the frequency of oscillation becomes.
supporting img

1 \(2 f\)
2 \(f / 2\)
3 \(f / 4\)
4 \(4 f\)
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PHXI14:OSCILLATIONS

364368 The pulley shown in the figure. has a radius \(r\), moment of inertia \(I\) about its axis and mass \(m\). Find the time period of vertical oscillations of its centre of mass. the spring constant of spring is \(K\) and the spring does not slip over the pulley.
supporting img

1 \(\pi \sqrt{\dfrac{m+I / R^{2}}{K}}\)
2 \(2 \pi \sqrt{\dfrac{m+I / R^{2}}{2 K}}\)
3 \(2 \pi \sqrt{\dfrac{2 m+I / R^{2}}{K}}\)
4 \(2 \pi \sqrt{\dfrac{m+I / R^{2}}{K}}\)
PHXI14:OSCILLATIONS

364369 Two identical springs of spring constant \(k\) each are connected in series and parallel as shown in figure. A mass \(M\) is suspended from them. The ratio of their frequencies of vertical oscillation will be
supporting img

1 \(1: 2\)
2 \(2: 1\)
3 \(4: 1\)
4 \(1: 4\)
PHXI14:OSCILLATIONS

364370 A body of mass \(m\) hangs from a smooth light fixed pulley \(P_{1}\) by the inextensible string fitted with the springs of stiffness \(k_{1}\) and \(k_{2}\). the string passes over the smooth light pulley \(P_{2}\) which is connected with another ideal spring of stiffness \(k_{2}\). Find the period of oscillation of the body.
supporting img

1 \(2 \pi \sqrt{m\left(\dfrac{1}{K_{1}}+\dfrac{4}{K_{2}}+\dfrac{1}{K_{3}}\right)}\)
2 \(2 \pi \sqrt{m\left(\dfrac{1}{K_{1}}+\dfrac{2}{K_{2}}+\dfrac{1}{K_{3}}\right)}\)
3 \({\rm{ }}2\pi \sqrt {m\left( {\frac{1}{{{K_1}}} + \frac{1}{{{K_2}}} + \frac{1}{{{K_3}}}} \right)} \)
4 \(2\pi \sqrt {m\left( {\frac{2}{{{K_1}}} + \frac{1}{{{K_2}}} + \frac{2}{{{K_3}}}} \right)} \)
PHXI14:OSCILLATIONS

364371 supporting img

1 A - P, B - Q, C - S, D - R
2 A - S, B - R, C - P, D - Q
3 A - R, B - P, C - S, D - Q
4 A - P, B - R, C - Q, D - S
PHXI14:OSCILLATIONS

364372 Two springs, of force constants \(k_{1}\) and \(k_{2}\) are connected to a mass \(m\) as shown. The frequency of oscillation of the mass is \(f\). If both \(k_{1}\) and \(k_{2}\) are made four times their original values, the frequency of oscillation becomes.
supporting img

1 \(2 f\)
2 \(f / 2\)
3 \(f / 4\)
4 \(4 f\)
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PHXI14:OSCILLATIONS

364368 The pulley shown in the figure. has a radius \(r\), moment of inertia \(I\) about its axis and mass \(m\). Find the time period of vertical oscillations of its centre of mass. the spring constant of spring is \(K\) and the spring does not slip over the pulley.
supporting img

1 \(\pi \sqrt{\dfrac{m+I / R^{2}}{K}}\)
2 \(2 \pi \sqrt{\dfrac{m+I / R^{2}}{2 K}}\)
3 \(2 \pi \sqrt{\dfrac{2 m+I / R^{2}}{K}}\)
4 \(2 \pi \sqrt{\dfrac{m+I / R^{2}}{K}}\)
PHXI14:OSCILLATIONS

364369 Two identical springs of spring constant \(k\) each are connected in series and parallel as shown in figure. A mass \(M\) is suspended from them. The ratio of their frequencies of vertical oscillation will be
supporting img

1 \(1: 2\)
2 \(2: 1\)
3 \(4: 1\)
4 \(1: 4\)
PHXI14:OSCILLATIONS

364370 A body of mass \(m\) hangs from a smooth light fixed pulley \(P_{1}\) by the inextensible string fitted with the springs of stiffness \(k_{1}\) and \(k_{2}\). the string passes over the smooth light pulley \(P_{2}\) which is connected with another ideal spring of stiffness \(k_{2}\). Find the period of oscillation of the body.
supporting img

1 \(2 \pi \sqrt{m\left(\dfrac{1}{K_{1}}+\dfrac{4}{K_{2}}+\dfrac{1}{K_{3}}\right)}\)
2 \(2 \pi \sqrt{m\left(\dfrac{1}{K_{1}}+\dfrac{2}{K_{2}}+\dfrac{1}{K_{3}}\right)}\)
3 \({\rm{ }}2\pi \sqrt {m\left( {\frac{1}{{{K_1}}} + \frac{1}{{{K_2}}} + \frac{1}{{{K_3}}}} \right)} \)
4 \(2\pi \sqrt {m\left( {\frac{2}{{{K_1}}} + \frac{1}{{{K_2}}} + \frac{2}{{{K_3}}}} \right)} \)
PHXI14:OSCILLATIONS

364371 supporting img

1 A - P, B - Q, C - S, D - R
2 A - S, B - R, C - P, D - Q
3 A - R, B - P, C - S, D - Q
4 A - P, B - R, C - Q, D - S
PHXI14:OSCILLATIONS

364372 Two springs, of force constants \(k_{1}\) and \(k_{2}\) are connected to a mass \(m\) as shown. The frequency of oscillation of the mass is \(f\). If both \(k_{1}\) and \(k_{2}\) are made four times their original values, the frequency of oscillation becomes.
supporting img

1 \(2 f\)
2 \(f / 2\)
3 \(f / 4\)
4 \(4 f\)