Energy of Oscillation
Oscillations

140360 A body of mass $1 \mathrm{~kg}$ is executing simple harmonic motion (SHM). Its displacement y(in cm) at time $t$ is given by $y=$ $\left[6 \sin \left(100 t+\frac{\pi}{4}\right)\right] \mathrm{cm}$. Its maximum kinetic energy is

1 $1.8 \mathrm{~J}$
2 $18 \mathrm{~J}$
3 $180 \mathrm{~J}$
4 $0.18 \mathrm{~J}$
Oscillations

140361 A body performing simple harmonic motion has potential energy ' $P_{1}$ ' at displacement ' $x_{1}$ '. Its potential energy is ' $P_{2}$ ' at displacement ' $x_{2}$ '. The potential energy ' $P$ ' at displacement $\left(\mathbf{x}_{1}+\mathbf{x}_{2}\right)$ is

1 $\mathrm{P}_{1}+\mathrm{P}_{2}$
2 $\mathrm{P}_{1}+\mathrm{P}_{2}+2 \sqrt{\mathrm{P}_{1} \mathrm{P}_{2}}$
3 $\sqrt{\mathrm{P}_{1} \mathrm{P}_{2}}$
4 $\sqrt{\mathrm{P}_{1}^{2}+\mathrm{P}_{2}^{2}}$
Oscillations

140363 The kinetic energy, $K$ of a body performing simple harmonic motion varies with time $t$, is indicated in graph

1
2
3
4
Oscillations

140364 The ratio of kinetic energy to the potential energy of a particle executing S.H.M. at a distance equal to $(1 / 3) \mathrm{rd}$ of its amplitude is

1 $9: 1$
2 $2: 1$
3 $8: 1$
4 $3: 1$
Oscillations

140366 A particle of mass $0.1 \mathrm{~kg}$ is executing simple harmonic motion of amplitude $0.1 \mathrm{~m}$. When the particle passes through the mean position, its kinetic energy is $8 \times 10^{-3} \mathrm{~J}$. If the initial phase is $45^{\circ}$, the equation of its motion is (Assume, $x(t)$ as the position of the particle at time t.)

1 $x(t)=0.1 \sin \left(4 t+\frac{\pi}{4}\right)$
2 $x(t)=0.1 \sin \left(16 \mathrm{t}+\frac{\pi}{4}\right)$
3 $\text { } x(t)=0.1 \sin \left(2\left(t+\frac{\pi}{4}\right)\right)$
4 $\text { } x(t)=0.1 \sin \left(2 \mathrm{t}+\frac{\pi}{4}\right)$
Oscillations

140360 A body of mass $1 \mathrm{~kg}$ is executing simple harmonic motion (SHM). Its displacement y(in cm) at time $t$ is given by $y=$ $\left[6 \sin \left(100 t+\frac{\pi}{4}\right)\right] \mathrm{cm}$. Its maximum kinetic energy is

1 $1.8 \mathrm{~J}$
2 $18 \mathrm{~J}$
3 $180 \mathrm{~J}$
4 $0.18 \mathrm{~J}$
Oscillations

140361 A body performing simple harmonic motion has potential energy ' $P_{1}$ ' at displacement ' $x_{1}$ '. Its potential energy is ' $P_{2}$ ' at displacement ' $x_{2}$ '. The potential energy ' $P$ ' at displacement $\left(\mathbf{x}_{1}+\mathbf{x}_{2}\right)$ is

1 $\mathrm{P}_{1}+\mathrm{P}_{2}$
2 $\mathrm{P}_{1}+\mathrm{P}_{2}+2 \sqrt{\mathrm{P}_{1} \mathrm{P}_{2}}$
3 $\sqrt{\mathrm{P}_{1} \mathrm{P}_{2}}$
4 $\sqrt{\mathrm{P}_{1}^{2}+\mathrm{P}_{2}^{2}}$
Oscillations

140363 The kinetic energy, $K$ of a body performing simple harmonic motion varies with time $t$, is indicated in graph

1
2
3
4
Oscillations

140364 The ratio of kinetic energy to the potential energy of a particle executing S.H.M. at a distance equal to $(1 / 3) \mathrm{rd}$ of its amplitude is

1 $9: 1$
2 $2: 1$
3 $8: 1$
4 $3: 1$
Oscillations

140366 A particle of mass $0.1 \mathrm{~kg}$ is executing simple harmonic motion of amplitude $0.1 \mathrm{~m}$. When the particle passes through the mean position, its kinetic energy is $8 \times 10^{-3} \mathrm{~J}$. If the initial phase is $45^{\circ}$, the equation of its motion is (Assume, $x(t)$ as the position of the particle at time t.)

1 $x(t)=0.1 \sin \left(4 t+\frac{\pi}{4}\right)$
2 $x(t)=0.1 \sin \left(16 \mathrm{t}+\frac{\pi}{4}\right)$
3 $\text { } x(t)=0.1 \sin \left(2\left(t+\frac{\pi}{4}\right)\right)$
4 $\text { } x(t)=0.1 \sin \left(2 \mathrm{t}+\frac{\pi}{4}\right)$
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Oscillations

140360 A body of mass $1 \mathrm{~kg}$ is executing simple harmonic motion (SHM). Its displacement y(in cm) at time $t$ is given by $y=$ $\left[6 \sin \left(100 t+\frac{\pi}{4}\right)\right] \mathrm{cm}$. Its maximum kinetic energy is

1 $1.8 \mathrm{~J}$
2 $18 \mathrm{~J}$
3 $180 \mathrm{~J}$
4 $0.18 \mathrm{~J}$
Oscillations

140361 A body performing simple harmonic motion has potential energy ' $P_{1}$ ' at displacement ' $x_{1}$ '. Its potential energy is ' $P_{2}$ ' at displacement ' $x_{2}$ '. The potential energy ' $P$ ' at displacement $\left(\mathbf{x}_{1}+\mathbf{x}_{2}\right)$ is

1 $\mathrm{P}_{1}+\mathrm{P}_{2}$
2 $\mathrm{P}_{1}+\mathrm{P}_{2}+2 \sqrt{\mathrm{P}_{1} \mathrm{P}_{2}}$
3 $\sqrt{\mathrm{P}_{1} \mathrm{P}_{2}}$
4 $\sqrt{\mathrm{P}_{1}^{2}+\mathrm{P}_{2}^{2}}$
Oscillations

140363 The kinetic energy, $K$ of a body performing simple harmonic motion varies with time $t$, is indicated in graph

1
2
3
4
Oscillations

140364 The ratio of kinetic energy to the potential energy of a particle executing S.H.M. at a distance equal to $(1 / 3) \mathrm{rd}$ of its amplitude is

1 $9: 1$
2 $2: 1$
3 $8: 1$
4 $3: 1$
Oscillations

140366 A particle of mass $0.1 \mathrm{~kg}$ is executing simple harmonic motion of amplitude $0.1 \mathrm{~m}$. When the particle passes through the mean position, its kinetic energy is $8 \times 10^{-3} \mathrm{~J}$. If the initial phase is $45^{\circ}$, the equation of its motion is (Assume, $x(t)$ as the position of the particle at time t.)

1 $x(t)=0.1 \sin \left(4 t+\frac{\pi}{4}\right)$
2 $x(t)=0.1 \sin \left(16 \mathrm{t}+\frac{\pi}{4}\right)$
3 $\text { } x(t)=0.1 \sin \left(2\left(t+\frac{\pi}{4}\right)\right)$
4 $\text { } x(t)=0.1 \sin \left(2 \mathrm{t}+\frac{\pi}{4}\right)$
Oscillations

140360 A body of mass $1 \mathrm{~kg}$ is executing simple harmonic motion (SHM). Its displacement y(in cm) at time $t$ is given by $y=$ $\left[6 \sin \left(100 t+\frac{\pi}{4}\right)\right] \mathrm{cm}$. Its maximum kinetic energy is

1 $1.8 \mathrm{~J}$
2 $18 \mathrm{~J}$
3 $180 \mathrm{~J}$
4 $0.18 \mathrm{~J}$
Oscillations

140361 A body performing simple harmonic motion has potential energy ' $P_{1}$ ' at displacement ' $x_{1}$ '. Its potential energy is ' $P_{2}$ ' at displacement ' $x_{2}$ '. The potential energy ' $P$ ' at displacement $\left(\mathbf{x}_{1}+\mathbf{x}_{2}\right)$ is

1 $\mathrm{P}_{1}+\mathrm{P}_{2}$
2 $\mathrm{P}_{1}+\mathrm{P}_{2}+2 \sqrt{\mathrm{P}_{1} \mathrm{P}_{2}}$
3 $\sqrt{\mathrm{P}_{1} \mathrm{P}_{2}}$
4 $\sqrt{\mathrm{P}_{1}^{2}+\mathrm{P}_{2}^{2}}$
Oscillations

140363 The kinetic energy, $K$ of a body performing simple harmonic motion varies with time $t$, is indicated in graph

1
2
3
4
Oscillations

140364 The ratio of kinetic energy to the potential energy of a particle executing S.H.M. at a distance equal to $(1 / 3) \mathrm{rd}$ of its amplitude is

1 $9: 1$
2 $2: 1$
3 $8: 1$
4 $3: 1$
Oscillations

140366 A particle of mass $0.1 \mathrm{~kg}$ is executing simple harmonic motion of amplitude $0.1 \mathrm{~m}$. When the particle passes through the mean position, its kinetic energy is $8 \times 10^{-3} \mathrm{~J}$. If the initial phase is $45^{\circ}$, the equation of its motion is (Assume, $x(t)$ as the position of the particle at time t.)

1 $x(t)=0.1 \sin \left(4 t+\frac{\pi}{4}\right)$
2 $x(t)=0.1 \sin \left(16 \mathrm{t}+\frac{\pi}{4}\right)$
3 $\text { } x(t)=0.1 \sin \left(2\left(t+\frac{\pi}{4}\right)\right)$
4 $\text { } x(t)=0.1 \sin \left(2 \mathrm{t}+\frac{\pi}{4}\right)$
Oscillations

140360 A body of mass $1 \mathrm{~kg}$ is executing simple harmonic motion (SHM). Its displacement y(in cm) at time $t$ is given by $y=$ $\left[6 \sin \left(100 t+\frac{\pi}{4}\right)\right] \mathrm{cm}$. Its maximum kinetic energy is

1 $1.8 \mathrm{~J}$
2 $18 \mathrm{~J}$
3 $180 \mathrm{~J}$
4 $0.18 \mathrm{~J}$
Oscillations

140361 A body performing simple harmonic motion has potential energy ' $P_{1}$ ' at displacement ' $x_{1}$ '. Its potential energy is ' $P_{2}$ ' at displacement ' $x_{2}$ '. The potential energy ' $P$ ' at displacement $\left(\mathbf{x}_{1}+\mathbf{x}_{2}\right)$ is

1 $\mathrm{P}_{1}+\mathrm{P}_{2}$
2 $\mathrm{P}_{1}+\mathrm{P}_{2}+2 \sqrt{\mathrm{P}_{1} \mathrm{P}_{2}}$
3 $\sqrt{\mathrm{P}_{1} \mathrm{P}_{2}}$
4 $\sqrt{\mathrm{P}_{1}^{2}+\mathrm{P}_{2}^{2}}$
Oscillations

140363 The kinetic energy, $K$ of a body performing simple harmonic motion varies with time $t$, is indicated in graph

1
2
3
4
Oscillations

140364 The ratio of kinetic energy to the potential energy of a particle executing S.H.M. at a distance equal to $(1 / 3) \mathrm{rd}$ of its amplitude is

1 $9: 1$
2 $2: 1$
3 $8: 1$
4 $3: 1$
Oscillations

140366 A particle of mass $0.1 \mathrm{~kg}$ is executing simple harmonic motion of amplitude $0.1 \mathrm{~m}$. When the particle passes through the mean position, its kinetic energy is $8 \times 10^{-3} \mathrm{~J}$. If the initial phase is $45^{\circ}$, the equation of its motion is (Assume, $x(t)$ as the position of the particle at time t.)

1 $x(t)=0.1 \sin \left(4 t+\frac{\pi}{4}\right)$
2 $x(t)=0.1 \sin \left(16 \mathrm{t}+\frac{\pi}{4}\right)$
3 $\text { } x(t)=0.1 \sin \left(2\left(t+\frac{\pi}{4}\right)\right)$
4 $\text { } x(t)=0.1 \sin \left(2 \mathrm{t}+\frac{\pi}{4}\right)$