Some Systems Executing Simple Harmonic Motion
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PHXI14:OSCILLATIONS

364415 A spring of mass \(m\) is connected to a rigid support as shown in the figure. If the free end of the spring is given velocity \(v_{o}\) then kinetic energy of the spring is
supporting img

1 \(\dfrac{m v_{o}^{2}}{4}\)
2 \(\dfrac{m v_{o}^{2}}{3}\)
3 \(\dfrac{1}{2}\left(\dfrac{m}{3}\right) v_{o}^{2}\)
4 \(\dfrac{1}{2} m v_{o}^{2}\)
PHXI14:OSCILLATIONS

364416 Two bodies \({M}\) and \({N}\) of equal masses are suspended from two separate springs of constants \({k_{1}}\) and \({k_{2}}\) respectively. If \({M}\) and \({N}\) oscillate vertically so that their maximum velocities are equal, the ratio of amplitude of vibration of \({M}\) to that of \({N}\) is

1 \({\dfrac{k_{2}}{k_{1}}}\)
2 \({\dfrac{k_{1}}{k_{2}}}\)
3 \({\sqrt{\dfrac{k_{2}}{k_{1}}}}\)
4 \({\sqrt{\dfrac{k_{1}}{k_{2}}}}\)
PHXI14:OSCILLATIONS

364417 One-fourth length of a spring of force constant \(k\) is cut away: The force constant of the remaining spring will be

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

364418 A uniform disc of mass \(m = 2\;kg\) and radius \(R = 5\;cm\) is pivoted smoothly at its centre of mass. A light spring of stiffness \(k\) is attached with the disc tangentially (as shown in figure). Find the angular frequency of torsional oscillation of the disc is
(Take \(k = 5N/s,\sqrt 5 = 2.23)\)
supporting img

1 \(1.67\,rad/s\)
2 \(4.25\,rad/s\)
3 \(2.23\,rad/s\)
4 \(7.35\,rad/s\)
PHXI14:OSCILLATIONS

364419 A block of mass \(m\) attached to one end of the vertical spring produces extension \(x\). If the block is pulled and released, the periodic time of oscillation is

1 \(2 \pi \sqrt{\dfrac{x}{4 g}}\)
2 \(2 \pi \sqrt{\dfrac{2 x}{g}}\)
3 \(2 \pi \sqrt{\dfrac{x}{2 g}}\)
4 \(2 \pi \sqrt{\dfrac{x}{g}}\)
MHTCET - 2020
NEET DIGITAL LIBRARY
PHXI14:OSCILLATIONS

364415 A spring of mass \(m\) is connected to a rigid support as shown in the figure. If the free end of the spring is given velocity \(v_{o}\) then kinetic energy of the spring is
supporting img

1 \(\dfrac{m v_{o}^{2}}{4}\)
2 \(\dfrac{m v_{o}^{2}}{3}\)
3 \(\dfrac{1}{2}\left(\dfrac{m}{3}\right) v_{o}^{2}\)
4 \(\dfrac{1}{2} m v_{o}^{2}\)
PHXI14:OSCILLATIONS

364416 Two bodies \({M}\) and \({N}\) of equal masses are suspended from two separate springs of constants \({k_{1}}\) and \({k_{2}}\) respectively. If \({M}\) and \({N}\) oscillate vertically so that their maximum velocities are equal, the ratio of amplitude of vibration of \({M}\) to that of \({N}\) is

1 \({\dfrac{k_{2}}{k_{1}}}\)
2 \({\dfrac{k_{1}}{k_{2}}}\)
3 \({\sqrt{\dfrac{k_{2}}{k_{1}}}}\)
4 \({\sqrt{\dfrac{k_{1}}{k_{2}}}}\)
PHXI14:OSCILLATIONS

364417 One-fourth length of a spring of force constant \(k\) is cut away: The force constant of the remaining spring will be

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

364418 A uniform disc of mass \(m = 2\;kg\) and radius \(R = 5\;cm\) is pivoted smoothly at its centre of mass. A light spring of stiffness \(k\) is attached with the disc tangentially (as shown in figure). Find the angular frequency of torsional oscillation of the disc is
(Take \(k = 5N/s,\sqrt 5 = 2.23)\)
supporting img

1 \(1.67\,rad/s\)
2 \(4.25\,rad/s\)
3 \(2.23\,rad/s\)
4 \(7.35\,rad/s\)
PHXI14:OSCILLATIONS

364419 A block of mass \(m\) attached to one end of the vertical spring produces extension \(x\). If the block is pulled and released, the periodic time of oscillation is

1 \(2 \pi \sqrt{\dfrac{x}{4 g}}\)
2 \(2 \pi \sqrt{\dfrac{2 x}{g}}\)
3 \(2 \pi \sqrt{\dfrac{x}{2 g}}\)
4 \(2 \pi \sqrt{\dfrac{x}{g}}\)
MHTCET - 2020
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PHXI14:OSCILLATIONS

364415 A spring of mass \(m\) is connected to a rigid support as shown in the figure. If the free end of the spring is given velocity \(v_{o}\) then kinetic energy of the spring is
supporting img

1 \(\dfrac{m v_{o}^{2}}{4}\)
2 \(\dfrac{m v_{o}^{2}}{3}\)
3 \(\dfrac{1}{2}\left(\dfrac{m}{3}\right) v_{o}^{2}\)
4 \(\dfrac{1}{2} m v_{o}^{2}\)
PHXI14:OSCILLATIONS

364416 Two bodies \({M}\) and \({N}\) of equal masses are suspended from two separate springs of constants \({k_{1}}\) and \({k_{2}}\) respectively. If \({M}\) and \({N}\) oscillate vertically so that their maximum velocities are equal, the ratio of amplitude of vibration of \({M}\) to that of \({N}\) is

1 \({\dfrac{k_{2}}{k_{1}}}\)
2 \({\dfrac{k_{1}}{k_{2}}}\)
3 \({\sqrt{\dfrac{k_{2}}{k_{1}}}}\)
4 \({\sqrt{\dfrac{k_{1}}{k_{2}}}}\)
PHXI14:OSCILLATIONS

364417 One-fourth length of a spring of force constant \(k\) is cut away: The force constant of the remaining spring will be

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

364418 A uniform disc of mass \(m = 2\;kg\) and radius \(R = 5\;cm\) is pivoted smoothly at its centre of mass. A light spring of stiffness \(k\) is attached with the disc tangentially (as shown in figure). Find the angular frequency of torsional oscillation of the disc is
(Take \(k = 5N/s,\sqrt 5 = 2.23)\)
supporting img

1 \(1.67\,rad/s\)
2 \(4.25\,rad/s\)
3 \(2.23\,rad/s\)
4 \(7.35\,rad/s\)
PHXI14:OSCILLATIONS

364419 A block of mass \(m\) attached to one end of the vertical spring produces extension \(x\). If the block is pulled and released, the periodic time of oscillation is

1 \(2 \pi \sqrt{\dfrac{x}{4 g}}\)
2 \(2 \pi \sqrt{\dfrac{2 x}{g}}\)
3 \(2 \pi \sqrt{\dfrac{x}{2 g}}\)
4 \(2 \pi \sqrt{\dfrac{x}{g}}\)
MHTCET - 2020
For More Updates join with Us
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PHXI14:OSCILLATIONS

364415 A spring of mass \(m\) is connected to a rigid support as shown in the figure. If the free end of the spring is given velocity \(v_{o}\) then kinetic energy of the spring is
supporting img

1 \(\dfrac{m v_{o}^{2}}{4}\)
2 \(\dfrac{m v_{o}^{2}}{3}\)
3 \(\dfrac{1}{2}\left(\dfrac{m}{3}\right) v_{o}^{2}\)
4 \(\dfrac{1}{2} m v_{o}^{2}\)
PHXI14:OSCILLATIONS

364416 Two bodies \({M}\) and \({N}\) of equal masses are suspended from two separate springs of constants \({k_{1}}\) and \({k_{2}}\) respectively. If \({M}\) and \({N}\) oscillate vertically so that their maximum velocities are equal, the ratio of amplitude of vibration of \({M}\) to that of \({N}\) is

1 \({\dfrac{k_{2}}{k_{1}}}\)
2 \({\dfrac{k_{1}}{k_{2}}}\)
3 \({\sqrt{\dfrac{k_{2}}{k_{1}}}}\)
4 \({\sqrt{\dfrac{k_{1}}{k_{2}}}}\)
PHXI14:OSCILLATIONS

364417 One-fourth length of a spring of force constant \(k\) is cut away: The force constant of the remaining spring will be

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

364418 A uniform disc of mass \(m = 2\;kg\) and radius \(R = 5\;cm\) is pivoted smoothly at its centre of mass. A light spring of stiffness \(k\) is attached with the disc tangentially (as shown in figure). Find the angular frequency of torsional oscillation of the disc is
(Take \(k = 5N/s,\sqrt 5 = 2.23)\)
supporting img

1 \(1.67\,rad/s\)
2 \(4.25\,rad/s\)
3 \(2.23\,rad/s\)
4 \(7.35\,rad/s\)
PHXI14:OSCILLATIONS

364419 A block of mass \(m\) attached to one end of the vertical spring produces extension \(x\). If the block is pulled and released, the periodic time of oscillation is

1 \(2 \pi \sqrt{\dfrac{x}{4 g}}\)
2 \(2 \pi \sqrt{\dfrac{2 x}{g}}\)
3 \(2 \pi \sqrt{\dfrac{x}{2 g}}\)
4 \(2 \pi \sqrt{\dfrac{x}{g}}\)
MHTCET - 2020
NEET DIGITAL LIBRARY
PHXI14:OSCILLATIONS

364415 A spring of mass \(m\) is connected to a rigid support as shown in the figure. If the free end of the spring is given velocity \(v_{o}\) then kinetic energy of the spring is
supporting img

1 \(\dfrac{m v_{o}^{2}}{4}\)
2 \(\dfrac{m v_{o}^{2}}{3}\)
3 \(\dfrac{1}{2}\left(\dfrac{m}{3}\right) v_{o}^{2}\)
4 \(\dfrac{1}{2} m v_{o}^{2}\)
PHXI14:OSCILLATIONS

364416 Two bodies \({M}\) and \({N}\) of equal masses are suspended from two separate springs of constants \({k_{1}}\) and \({k_{2}}\) respectively. If \({M}\) and \({N}\) oscillate vertically so that their maximum velocities are equal, the ratio of amplitude of vibration of \({M}\) to that of \({N}\) is

1 \({\dfrac{k_{2}}{k_{1}}}\)
2 \({\dfrac{k_{1}}{k_{2}}}\)
3 \({\sqrt{\dfrac{k_{2}}{k_{1}}}}\)
4 \({\sqrt{\dfrac{k_{1}}{k_{2}}}}\)
PHXI14:OSCILLATIONS

364417 One-fourth length of a spring of force constant \(k\) is cut away: The force constant of the remaining spring will be

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

364418 A uniform disc of mass \(m = 2\;kg\) and radius \(R = 5\;cm\) is pivoted smoothly at its centre of mass. A light spring of stiffness \(k\) is attached with the disc tangentially (as shown in figure). Find the angular frequency of torsional oscillation of the disc is
(Take \(k = 5N/s,\sqrt 5 = 2.23)\)
supporting img

1 \(1.67\,rad/s\)
2 \(4.25\,rad/s\)
3 \(2.23\,rad/s\)
4 \(7.35\,rad/s\)
PHXI14:OSCILLATIONS

364419 A block of mass \(m\) attached to one end of the vertical spring produces extension \(x\). If the block is pulled and released, the periodic time of oscillation is

1 \(2 \pi \sqrt{\dfrac{x}{4 g}}\)
2 \(2 \pi \sqrt{\dfrac{2 x}{g}}\)
3 \(2 \pi \sqrt{\dfrac{x}{2 g}}\)
4 \(2 \pi \sqrt{\dfrac{x}{g}}\)
MHTCET - 2020