Force, Energy and their relation in Simple Harmonic Motion
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PHXI14:OSCILLATIONS

364133 A body is executing simple harmonic motion. At a displacement \(x\) its potential energy is \(E_{1}\) and at a displacement \(y\) its potential energy is \(E_{2}\). The potential energy \(E\) at displacement \((x+y)\) is

1 \(\sqrt{E}=\sqrt{E_{1}}+\sqrt{E_{2}}\)
2 \(\sqrt{E}=\sqrt{E_{1}}-\sqrt{E_{2}}\)
3 \(E=E_{1}+E_{2}\)
4 \(E=E_{1}-E_{2}\)
PHXI14:OSCILLATIONS

364134 A particle of mass \(m\) is executing oscillations about the origin on the \(x\) - axis. Its potential energy is \(U(x)=k[x]^{3}\), where \(k\) is a positive constant. If the amplitude of oscillation is \(a\), then its time period \(T\) is

1 independent of \(a\)
2 proportional to \(\dfrac{1}{\sqrt{a}}\)
3 proportional to \(a^{3 / 2}\)
4 proportional to \(\sqrt{a}\)
PHXI14:OSCILLATIONS

364135 Total energy of a particle executing S.H.M. is ( \(x\) is displacement from mean position):

1 Proportional to \(x^{2}\)
2 Proportional to \(x\)
3 Proportional to \(x^{1 / 2}\)
4 Independent of \(x\)
PHXI14:OSCILLATIONS

364136 Starting from the origin, a body oscillates simple harmonically with a period of \(2\,\sec \). After what time will its kinetic energy be \(75 \%\) of the total energy?

1 \(1{\rm{/}}12\,\sec \)
2 \(1{\rm{/}}6\,\sec \)
3 \(1{\rm{/}}4\,\sec \)
4 \(1{\rm{/}}3\,\sec \)
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PHXI14:OSCILLATIONS

364133 A body is executing simple harmonic motion. At a displacement \(x\) its potential energy is \(E_{1}\) and at a displacement \(y\) its potential energy is \(E_{2}\). The potential energy \(E\) at displacement \((x+y)\) is

1 \(\sqrt{E}=\sqrt{E_{1}}+\sqrt{E_{2}}\)
2 \(\sqrt{E}=\sqrt{E_{1}}-\sqrt{E_{2}}\)
3 \(E=E_{1}+E_{2}\)
4 \(E=E_{1}-E_{2}\)
PHXI14:OSCILLATIONS

364134 A particle of mass \(m\) is executing oscillations about the origin on the \(x\) - axis. Its potential energy is \(U(x)=k[x]^{3}\), where \(k\) is a positive constant. If the amplitude of oscillation is \(a\), then its time period \(T\) is

1 independent of \(a\)
2 proportional to \(\dfrac{1}{\sqrt{a}}\)
3 proportional to \(a^{3 / 2}\)
4 proportional to \(\sqrt{a}\)
PHXI14:OSCILLATIONS

364135 Total energy of a particle executing S.H.M. is ( \(x\) is displacement from mean position):

1 Proportional to \(x^{2}\)
2 Proportional to \(x\)
3 Proportional to \(x^{1 / 2}\)
4 Independent of \(x\)
PHXI14:OSCILLATIONS

364136 Starting from the origin, a body oscillates simple harmonically with a period of \(2\,\sec \). After what time will its kinetic energy be \(75 \%\) of the total energy?

1 \(1{\rm{/}}12\,\sec \)
2 \(1{\rm{/}}6\,\sec \)
3 \(1{\rm{/}}4\,\sec \)
4 \(1{\rm{/}}3\,\sec \)
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PHXI14:OSCILLATIONS

364133 A body is executing simple harmonic motion. At a displacement \(x\) its potential energy is \(E_{1}\) and at a displacement \(y\) its potential energy is \(E_{2}\). The potential energy \(E\) at displacement \((x+y)\) is

1 \(\sqrt{E}=\sqrt{E_{1}}+\sqrt{E_{2}}\)
2 \(\sqrt{E}=\sqrt{E_{1}}-\sqrt{E_{2}}\)
3 \(E=E_{1}+E_{2}\)
4 \(E=E_{1}-E_{2}\)
PHXI14:OSCILLATIONS

364134 A particle of mass \(m\) is executing oscillations about the origin on the \(x\) - axis. Its potential energy is \(U(x)=k[x]^{3}\), where \(k\) is a positive constant. If the amplitude of oscillation is \(a\), then its time period \(T\) is

1 independent of \(a\)
2 proportional to \(\dfrac{1}{\sqrt{a}}\)
3 proportional to \(a^{3 / 2}\)
4 proportional to \(\sqrt{a}\)
PHXI14:OSCILLATIONS

364135 Total energy of a particle executing S.H.M. is ( \(x\) is displacement from mean position):

1 Proportional to \(x^{2}\)
2 Proportional to \(x\)
3 Proportional to \(x^{1 / 2}\)
4 Independent of \(x\)
PHXI14:OSCILLATIONS

364136 Starting from the origin, a body oscillates simple harmonically with a period of \(2\,\sec \). After what time will its kinetic energy be \(75 \%\) of the total energy?

1 \(1{\rm{/}}12\,\sec \)
2 \(1{\rm{/}}6\,\sec \)
3 \(1{\rm{/}}4\,\sec \)
4 \(1{\rm{/}}3\,\sec \)
NEET DIGITAL LIBRARY
PHXI14:OSCILLATIONS

364133 A body is executing simple harmonic motion. At a displacement \(x\) its potential energy is \(E_{1}\) and at a displacement \(y\) its potential energy is \(E_{2}\). The potential energy \(E\) at displacement \((x+y)\) is

1 \(\sqrt{E}=\sqrt{E_{1}}+\sqrt{E_{2}}\)
2 \(\sqrt{E}=\sqrt{E_{1}}-\sqrt{E_{2}}\)
3 \(E=E_{1}+E_{2}\)
4 \(E=E_{1}-E_{2}\)
PHXI14:OSCILLATIONS

364134 A particle of mass \(m\) is executing oscillations about the origin on the \(x\) - axis. Its potential energy is \(U(x)=k[x]^{3}\), where \(k\) is a positive constant. If the amplitude of oscillation is \(a\), then its time period \(T\) is

1 independent of \(a\)
2 proportional to \(\dfrac{1}{\sqrt{a}}\)
3 proportional to \(a^{3 / 2}\)
4 proportional to \(\sqrt{a}\)
PHXI14:OSCILLATIONS

364135 Total energy of a particle executing S.H.M. is ( \(x\) is displacement from mean position):

1 Proportional to \(x^{2}\)
2 Proportional to \(x\)
3 Proportional to \(x^{1 / 2}\)
4 Independent of \(x\)
PHXI14:OSCILLATIONS

364136 Starting from the origin, a body oscillates simple harmonically with a period of \(2\,\sec \). After what time will its kinetic energy be \(75 \%\) of the total energy?

1 \(1{\rm{/}}12\,\sec \)
2 \(1{\rm{/}}6\,\sec \)
3 \(1{\rm{/}}4\,\sec \)
4 \(1{\rm{/}}3\,\sec \)
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