Some Systems Executing Simple Harmonic Motion
PHXI14:OSCILLATIONS

364398 A uniform cylinder of mass \(m=2 {~kg}\) and radius \(R=0.50\) \(m\) is in equilibrium on an inclined plane by the action of a light spring of stiffness \(K=300 {~N} / {m}\), gravity and reaction force acting on it. If the angle of inclination of the plane is \(\phi=30^{\circ}\), find the angular frequency of small oscillation of the cylinder.
supporting img

1 \(20\,rad/s\)
2 \(55\,rad/s\)
3 \(29\,rad/s\)
4 \(32\,rad/s\)
PHXI14:OSCILLATIONS

364399 A mass of \(0.2\;kg\) is attached to the lower end of a massless spring of force constant \(200\;N/m\), the upper end of which is fixed to a rigid support Which of the following statement is true?

1 In equilibrium, the spring will be stretched by \(1\;cm\)
2 If the mass is raised till the spring becomes unstretched and then released, it will go down by \(2\;cm\) before moving upwards
3 The frequency of oscillation will be nearly \(5\;Hz\)
4 All the above
PHXI14:OSCILLATIONS

364400 A mass \(m\) is hung on an ideal massless spring. Another equal mass is connected to the other end of the spring. the whole system is at rest. At \(t = 0,\;m\) is released and the system falls freely under gravity. Assume that natural length of the spring is \(L_{0}\), its initial stretched length is \(L\) and the acceleration due to gravity is \(g\). What is distance between masses as function of time?
supporting img

1 \(L_{0} \cos \sqrt{\dfrac{2 k}{m}} t\)
2 \(L_{0}+\left(L-L_{0}\right) \cos \sqrt{\dfrac{2 k}{m}} t\)
3 \(L_{0}+\left(L-L_{0}\right) \sin \sqrt{\dfrac{2 k}{m}} t\)
4 \(L_{0} \sin \sqrt{\dfrac{2 k}{m}} t\)
PHXI14:OSCILLATIONS

364401 A mass \(m_{1}\) connected to a horizontal spring perform SHM with amplitude \(A\). While mass \(m_{1}\) is passing through mean position, another mass \(m_{2}\) is placed on it so that both the masses move together with amplitude \(A_{1}\). The ratio of \(\dfrac{A_{1}}{A}\) is \(\left(m_{2} < m_{1}\right)\)

1 \(\left[\dfrac{m_{1}}{m_{1}+m_{2}}\right]^{\frac{1}{2}}\)
2 \(\left[\dfrac{m_{1}+m_{2}}{m_{1}}\right]^{\frac{1}{2}}\)
3 \(\left[\dfrac{m_{2}}{m_{1}+m_{2}}\right]^{\frac{1}{2}}\)
4 \(\left[\dfrac{m_{1}+m_{2}}{m_{2}}\right]^{\frac{1}{2}}\)
PHXI14:OSCILLATIONS

364402 A body of mass \(64\;g\) is made to oscillate turn by turn on two different springs \(A\) and \(B\). Spring \(A\) and \(B\) has force constant \(4 \dfrac{N}{m}\) and \(16 \dfrac{N}{m}\) respectively. If \(T_{1}\) and \(T_{2}\) are period of oscillations of spring \(A\) and \(B\) respectively, then \(\dfrac{T_{1}+T_{2}}{T_{1}-T_{2}}\) will be

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

364398 A uniform cylinder of mass \(m=2 {~kg}\) and radius \(R=0.50\) \(m\) is in equilibrium on an inclined plane by the action of a light spring of stiffness \(K=300 {~N} / {m}\), gravity and reaction force acting on it. If the angle of inclination of the plane is \(\phi=30^{\circ}\), find the angular frequency of small oscillation of the cylinder.
supporting img

1 \(20\,rad/s\)
2 \(55\,rad/s\)
3 \(29\,rad/s\)
4 \(32\,rad/s\)
PHXI14:OSCILLATIONS

364399 A mass of \(0.2\;kg\) is attached to the lower end of a massless spring of force constant \(200\;N/m\), the upper end of which is fixed to a rigid support Which of the following statement is true?

1 In equilibrium, the spring will be stretched by \(1\;cm\)
2 If the mass is raised till the spring becomes unstretched and then released, it will go down by \(2\;cm\) before moving upwards
3 The frequency of oscillation will be nearly \(5\;Hz\)
4 All the above
PHXI14:OSCILLATIONS

364400 A mass \(m\) is hung on an ideal massless spring. Another equal mass is connected to the other end of the spring. the whole system is at rest. At \(t = 0,\;m\) is released and the system falls freely under gravity. Assume that natural length of the spring is \(L_{0}\), its initial stretched length is \(L\) and the acceleration due to gravity is \(g\). What is distance between masses as function of time?
supporting img

1 \(L_{0} \cos \sqrt{\dfrac{2 k}{m}} t\)
2 \(L_{0}+\left(L-L_{0}\right) \cos \sqrt{\dfrac{2 k}{m}} t\)
3 \(L_{0}+\left(L-L_{0}\right) \sin \sqrt{\dfrac{2 k}{m}} t\)
4 \(L_{0} \sin \sqrt{\dfrac{2 k}{m}} t\)
PHXI14:OSCILLATIONS

364401 A mass \(m_{1}\) connected to a horizontal spring perform SHM with amplitude \(A\). While mass \(m_{1}\) is passing through mean position, another mass \(m_{2}\) is placed on it so that both the masses move together with amplitude \(A_{1}\). The ratio of \(\dfrac{A_{1}}{A}\) is \(\left(m_{2} < m_{1}\right)\)

1 \(\left[\dfrac{m_{1}}{m_{1}+m_{2}}\right]^{\frac{1}{2}}\)
2 \(\left[\dfrac{m_{1}+m_{2}}{m_{1}}\right]^{\frac{1}{2}}\)
3 \(\left[\dfrac{m_{2}}{m_{1}+m_{2}}\right]^{\frac{1}{2}}\)
4 \(\left[\dfrac{m_{1}+m_{2}}{m_{2}}\right]^{\frac{1}{2}}\)
PHXI14:OSCILLATIONS

364402 A body of mass \(64\;g\) is made to oscillate turn by turn on two different springs \(A\) and \(B\). Spring \(A\) and \(B\) has force constant \(4 \dfrac{N}{m}\) and \(16 \dfrac{N}{m}\) respectively. If \(T_{1}\) and \(T_{2}\) are period of oscillations of spring \(A\) and \(B\) respectively, then \(\dfrac{T_{1}+T_{2}}{T_{1}-T_{2}}\) will be

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

364398 A uniform cylinder of mass \(m=2 {~kg}\) and radius \(R=0.50\) \(m\) is in equilibrium on an inclined plane by the action of a light spring of stiffness \(K=300 {~N} / {m}\), gravity and reaction force acting on it. If the angle of inclination of the plane is \(\phi=30^{\circ}\), find the angular frequency of small oscillation of the cylinder.
supporting img

1 \(20\,rad/s\)
2 \(55\,rad/s\)
3 \(29\,rad/s\)
4 \(32\,rad/s\)
PHXI14:OSCILLATIONS

364399 A mass of \(0.2\;kg\) is attached to the lower end of a massless spring of force constant \(200\;N/m\), the upper end of which is fixed to a rigid support Which of the following statement is true?

1 In equilibrium, the spring will be stretched by \(1\;cm\)
2 If the mass is raised till the spring becomes unstretched and then released, it will go down by \(2\;cm\) before moving upwards
3 The frequency of oscillation will be nearly \(5\;Hz\)
4 All the above
PHXI14:OSCILLATIONS

364400 A mass \(m\) is hung on an ideal massless spring. Another equal mass is connected to the other end of the spring. the whole system is at rest. At \(t = 0,\;m\) is released and the system falls freely under gravity. Assume that natural length of the spring is \(L_{0}\), its initial stretched length is \(L\) and the acceleration due to gravity is \(g\). What is distance between masses as function of time?
supporting img

1 \(L_{0} \cos \sqrt{\dfrac{2 k}{m}} t\)
2 \(L_{0}+\left(L-L_{0}\right) \cos \sqrt{\dfrac{2 k}{m}} t\)
3 \(L_{0}+\left(L-L_{0}\right) \sin \sqrt{\dfrac{2 k}{m}} t\)
4 \(L_{0} \sin \sqrt{\dfrac{2 k}{m}} t\)
PHXI14:OSCILLATIONS

364401 A mass \(m_{1}\) connected to a horizontal spring perform SHM with amplitude \(A\). While mass \(m_{1}\) is passing through mean position, another mass \(m_{2}\) is placed on it so that both the masses move together with amplitude \(A_{1}\). The ratio of \(\dfrac{A_{1}}{A}\) is \(\left(m_{2} < m_{1}\right)\)

1 \(\left[\dfrac{m_{1}}{m_{1}+m_{2}}\right]^{\frac{1}{2}}\)
2 \(\left[\dfrac{m_{1}+m_{2}}{m_{1}}\right]^{\frac{1}{2}}\)
3 \(\left[\dfrac{m_{2}}{m_{1}+m_{2}}\right]^{\frac{1}{2}}\)
4 \(\left[\dfrac{m_{1}+m_{2}}{m_{2}}\right]^{\frac{1}{2}}\)
PHXI14:OSCILLATIONS

364402 A body of mass \(64\;g\) is made to oscillate turn by turn on two different springs \(A\) and \(B\). Spring \(A\) and \(B\) has force constant \(4 \dfrac{N}{m}\) and \(16 \dfrac{N}{m}\) respectively. If \(T_{1}\) and \(T_{2}\) are period of oscillations of spring \(A\) and \(B\) respectively, then \(\dfrac{T_{1}+T_{2}}{T_{1}-T_{2}}\) will be

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

364398 A uniform cylinder of mass \(m=2 {~kg}\) and radius \(R=0.50\) \(m\) is in equilibrium on an inclined plane by the action of a light spring of stiffness \(K=300 {~N} / {m}\), gravity and reaction force acting on it. If the angle of inclination of the plane is \(\phi=30^{\circ}\), find the angular frequency of small oscillation of the cylinder.
supporting img

1 \(20\,rad/s\)
2 \(55\,rad/s\)
3 \(29\,rad/s\)
4 \(32\,rad/s\)
PHXI14:OSCILLATIONS

364399 A mass of \(0.2\;kg\) is attached to the lower end of a massless spring of force constant \(200\;N/m\), the upper end of which is fixed to a rigid support Which of the following statement is true?

1 In equilibrium, the spring will be stretched by \(1\;cm\)
2 If the mass is raised till the spring becomes unstretched and then released, it will go down by \(2\;cm\) before moving upwards
3 The frequency of oscillation will be nearly \(5\;Hz\)
4 All the above
PHXI14:OSCILLATIONS

364400 A mass \(m\) is hung on an ideal massless spring. Another equal mass is connected to the other end of the spring. the whole system is at rest. At \(t = 0,\;m\) is released and the system falls freely under gravity. Assume that natural length of the spring is \(L_{0}\), its initial stretched length is \(L\) and the acceleration due to gravity is \(g\). What is distance between masses as function of time?
supporting img

1 \(L_{0} \cos \sqrt{\dfrac{2 k}{m}} t\)
2 \(L_{0}+\left(L-L_{0}\right) \cos \sqrt{\dfrac{2 k}{m}} t\)
3 \(L_{0}+\left(L-L_{0}\right) \sin \sqrt{\dfrac{2 k}{m}} t\)
4 \(L_{0} \sin \sqrt{\dfrac{2 k}{m}} t\)
PHXI14:OSCILLATIONS

364401 A mass \(m_{1}\) connected to a horizontal spring perform SHM with amplitude \(A\). While mass \(m_{1}\) is passing through mean position, another mass \(m_{2}\) is placed on it so that both the masses move together with amplitude \(A_{1}\). The ratio of \(\dfrac{A_{1}}{A}\) is \(\left(m_{2} < m_{1}\right)\)

1 \(\left[\dfrac{m_{1}}{m_{1}+m_{2}}\right]^{\frac{1}{2}}\)
2 \(\left[\dfrac{m_{1}+m_{2}}{m_{1}}\right]^{\frac{1}{2}}\)
3 \(\left[\dfrac{m_{2}}{m_{1}+m_{2}}\right]^{\frac{1}{2}}\)
4 \(\left[\dfrac{m_{1}+m_{2}}{m_{2}}\right]^{\frac{1}{2}}\)
PHXI14:OSCILLATIONS

364402 A body of mass \(64\;g\) is made to oscillate turn by turn on two different springs \(A\) and \(B\). Spring \(A\) and \(B\) has force constant \(4 \dfrac{N}{m}\) and \(16 \dfrac{N}{m}\) respectively. If \(T_{1}\) and \(T_{2}\) are period of oscillations of spring \(A\) and \(B\) respectively, then \(\dfrac{T_{1}+T_{2}}{T_{1}-T_{2}}\) will be

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

364398 A uniform cylinder of mass \(m=2 {~kg}\) and radius \(R=0.50\) \(m\) is in equilibrium on an inclined plane by the action of a light spring of stiffness \(K=300 {~N} / {m}\), gravity and reaction force acting on it. If the angle of inclination of the plane is \(\phi=30^{\circ}\), find the angular frequency of small oscillation of the cylinder.
supporting img

1 \(20\,rad/s\)
2 \(55\,rad/s\)
3 \(29\,rad/s\)
4 \(32\,rad/s\)
PHXI14:OSCILLATIONS

364399 A mass of \(0.2\;kg\) is attached to the lower end of a massless spring of force constant \(200\;N/m\), the upper end of which is fixed to a rigid support Which of the following statement is true?

1 In equilibrium, the spring will be stretched by \(1\;cm\)
2 If the mass is raised till the spring becomes unstretched and then released, it will go down by \(2\;cm\) before moving upwards
3 The frequency of oscillation will be nearly \(5\;Hz\)
4 All the above
PHXI14:OSCILLATIONS

364400 A mass \(m\) is hung on an ideal massless spring. Another equal mass is connected to the other end of the spring. the whole system is at rest. At \(t = 0,\;m\) is released and the system falls freely under gravity. Assume that natural length of the spring is \(L_{0}\), its initial stretched length is \(L\) and the acceleration due to gravity is \(g\). What is distance between masses as function of time?
supporting img

1 \(L_{0} \cos \sqrt{\dfrac{2 k}{m}} t\)
2 \(L_{0}+\left(L-L_{0}\right) \cos \sqrt{\dfrac{2 k}{m}} t\)
3 \(L_{0}+\left(L-L_{0}\right) \sin \sqrt{\dfrac{2 k}{m}} t\)
4 \(L_{0} \sin \sqrt{\dfrac{2 k}{m}} t\)
PHXI14:OSCILLATIONS

364401 A mass \(m_{1}\) connected to a horizontal spring perform SHM with amplitude \(A\). While mass \(m_{1}\) is passing through mean position, another mass \(m_{2}\) is placed on it so that both the masses move together with amplitude \(A_{1}\). The ratio of \(\dfrac{A_{1}}{A}\) is \(\left(m_{2} < m_{1}\right)\)

1 \(\left[\dfrac{m_{1}}{m_{1}+m_{2}}\right]^{\frac{1}{2}}\)
2 \(\left[\dfrac{m_{1}+m_{2}}{m_{1}}\right]^{\frac{1}{2}}\)
3 \(\left[\dfrac{m_{2}}{m_{1}+m_{2}}\right]^{\frac{1}{2}}\)
4 \(\left[\dfrac{m_{1}+m_{2}}{m_{2}}\right]^{\frac{1}{2}}\)
PHXI14:OSCILLATIONS

364402 A body of mass \(64\;g\) is made to oscillate turn by turn on two different springs \(A\) and \(B\). Spring \(A\) and \(B\) has force constant \(4 \dfrac{N}{m}\) and \(16 \dfrac{N}{m}\) respectively. If \(T_{1}\) and \(T_{2}\) are period of oscillations of spring \(A\) and \(B\) respectively, then \(\dfrac{T_{1}+T_{2}}{T_{1}-T_{2}}\) will be

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