Energy of Oscillation
Oscillations

140398 The angular velocity and the amplitude of a simple pendulum is $\omega$ and $A$ respectively. At a displacement $x$ from the mean position, if its kinetic energy is $T$ and potential energy is $U$, then the ratio of $T$ to $U$ is

1 $\left(\frac{\mathrm{A}^{2}-\mathrm{x}^{2} \omega^{2}}{\mathrm{x}^{2} \omega^{2}}\right)$
2 $\left(\frac{x^{2} \omega^{2}}{A^{2}-x^{2} \omega^{2}}\right)$
3 $\frac{\left(A^{2}-x^{2}\right)}{x^{2}}$
4 $\frac{x^{2}}{\left(A^{2}-x^{2}\right)}$
Oscillations

140399 In $\mathrm{SHM}$ restoring force is $\mathrm{F}=-\mathrm{kx}$, where $\mathrm{k}$ is force constant, $x$ is displacement and $A$ is amplitude of motion, then total energy depends upon

1 $\mathrm{k}, \mathrm{A}$ and $\mathrm{m}$
2 $\mathrm{k}, \mathrm{x}, \mathrm{m}$
3 $\mathrm{k}, \mathrm{A}$
4 $\mathrm{k}, \mathrm{x}$
Oscillations

140400 The oscillation of a body on a smooth horizontal surface is represented by the equation,
$X=A \cos (\omega t)$
Where, $X=$ displacement at time $t$
$\omega=\text { frequency of oscillation }$
Which one of the following graphs shows correctly the variation a with $t$ ?

1
2
3
4
Here, $\mathbf{a}=$ acceleration at time $t$
$\mathbf{T}=$ Time period
Oscillations

140401 The total mechanical energy of a harmonic oscillator of $A=1 \mathrm{~m}$ and force constant 200 $\mathrm{Nm}^{-1}$ is $150 \mathrm{~J}$. Then

1 the minimum PE is zero
2 the minimum PE is $100 \mathrm{~J}$
3 the minimum PE is $50 \mathrm{~J}$
4 the maximum $\mathrm{KE}$ is $150 \mathrm{~J}$
Oscillations

140404 A body is executing S.H.M. Its potential energy is $E_{1}$ and $E_{2}$ at displacement $x$ and $y$ respectively. The potential energy at displacement $(x+y)$ is

1 $\mathrm{E}_{1}-\mathrm{E}_{2}=\mathrm{E}$
2 $\sqrt{\mathrm{E}_{1}}-\sqrt{\mathrm{E}_{2}}=\sqrt{\mathrm{E}}$
3 $\mathrm{E}_{1}+\mathrm{E}_{2}=\mathrm{E}$
4 $\sqrt{\mathrm{E}_{1}}+\sqrt{\mathrm{E}_{2}}=\sqrt{\mathrm{E}}$
Oscillations

140398 The angular velocity and the amplitude of a simple pendulum is $\omega$ and $A$ respectively. At a displacement $x$ from the mean position, if its kinetic energy is $T$ and potential energy is $U$, then the ratio of $T$ to $U$ is

1 $\left(\frac{\mathrm{A}^{2}-\mathrm{x}^{2} \omega^{2}}{\mathrm{x}^{2} \omega^{2}}\right)$
2 $\left(\frac{x^{2} \omega^{2}}{A^{2}-x^{2} \omega^{2}}\right)$
3 $\frac{\left(A^{2}-x^{2}\right)}{x^{2}}$
4 $\frac{x^{2}}{\left(A^{2}-x^{2}\right)}$
Oscillations

140399 In $\mathrm{SHM}$ restoring force is $\mathrm{F}=-\mathrm{kx}$, where $\mathrm{k}$ is force constant, $x$ is displacement and $A$ is amplitude of motion, then total energy depends upon

1 $\mathrm{k}, \mathrm{A}$ and $\mathrm{m}$
2 $\mathrm{k}, \mathrm{x}, \mathrm{m}$
3 $\mathrm{k}, \mathrm{A}$
4 $\mathrm{k}, \mathrm{x}$
Oscillations

140400 The oscillation of a body on a smooth horizontal surface is represented by the equation,
$X=A \cos (\omega t)$
Where, $X=$ displacement at time $t$
$\omega=\text { frequency of oscillation }$
Which one of the following graphs shows correctly the variation a with $t$ ?

1
2
3
4
Here, $\mathbf{a}=$ acceleration at time $t$
$\mathbf{T}=$ Time period
Oscillations

140401 The total mechanical energy of a harmonic oscillator of $A=1 \mathrm{~m}$ and force constant 200 $\mathrm{Nm}^{-1}$ is $150 \mathrm{~J}$. Then

1 the minimum PE is zero
2 the minimum PE is $100 \mathrm{~J}$
3 the minimum PE is $50 \mathrm{~J}$
4 the maximum $\mathrm{KE}$ is $150 \mathrm{~J}$
Oscillations

140404 A body is executing S.H.M. Its potential energy is $E_{1}$ and $E_{2}$ at displacement $x$ and $y$ respectively. The potential energy at displacement $(x+y)$ is

1 $\mathrm{E}_{1}-\mathrm{E}_{2}=\mathrm{E}$
2 $\sqrt{\mathrm{E}_{1}}-\sqrt{\mathrm{E}_{2}}=\sqrt{\mathrm{E}}$
3 $\mathrm{E}_{1}+\mathrm{E}_{2}=\mathrm{E}$
4 $\sqrt{\mathrm{E}_{1}}+\sqrt{\mathrm{E}_{2}}=\sqrt{\mathrm{E}}$
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Oscillations

140398 The angular velocity and the amplitude of a simple pendulum is $\omega$ and $A$ respectively. At a displacement $x$ from the mean position, if its kinetic energy is $T$ and potential energy is $U$, then the ratio of $T$ to $U$ is

1 $\left(\frac{\mathrm{A}^{2}-\mathrm{x}^{2} \omega^{2}}{\mathrm{x}^{2} \omega^{2}}\right)$
2 $\left(\frac{x^{2} \omega^{2}}{A^{2}-x^{2} \omega^{2}}\right)$
3 $\frac{\left(A^{2}-x^{2}\right)}{x^{2}}$
4 $\frac{x^{2}}{\left(A^{2}-x^{2}\right)}$
Oscillations

140399 In $\mathrm{SHM}$ restoring force is $\mathrm{F}=-\mathrm{kx}$, where $\mathrm{k}$ is force constant, $x$ is displacement and $A$ is amplitude of motion, then total energy depends upon

1 $\mathrm{k}, \mathrm{A}$ and $\mathrm{m}$
2 $\mathrm{k}, \mathrm{x}, \mathrm{m}$
3 $\mathrm{k}, \mathrm{A}$
4 $\mathrm{k}, \mathrm{x}$
Oscillations

140400 The oscillation of a body on a smooth horizontal surface is represented by the equation,
$X=A \cos (\omega t)$
Where, $X=$ displacement at time $t$
$\omega=\text { frequency of oscillation }$
Which one of the following graphs shows correctly the variation a with $t$ ?

1
2
3
4
Here, $\mathbf{a}=$ acceleration at time $t$
$\mathbf{T}=$ Time period
Oscillations

140401 The total mechanical energy of a harmonic oscillator of $A=1 \mathrm{~m}$ and force constant 200 $\mathrm{Nm}^{-1}$ is $150 \mathrm{~J}$. Then

1 the minimum PE is zero
2 the minimum PE is $100 \mathrm{~J}$
3 the minimum PE is $50 \mathrm{~J}$
4 the maximum $\mathrm{KE}$ is $150 \mathrm{~J}$
Oscillations

140404 A body is executing S.H.M. Its potential energy is $E_{1}$ and $E_{2}$ at displacement $x$ and $y$ respectively. The potential energy at displacement $(x+y)$ is

1 $\mathrm{E}_{1}-\mathrm{E}_{2}=\mathrm{E}$
2 $\sqrt{\mathrm{E}_{1}}-\sqrt{\mathrm{E}_{2}}=\sqrt{\mathrm{E}}$
3 $\mathrm{E}_{1}+\mathrm{E}_{2}=\mathrm{E}$
4 $\sqrt{\mathrm{E}_{1}}+\sqrt{\mathrm{E}_{2}}=\sqrt{\mathrm{E}}$
Oscillations

140398 The angular velocity and the amplitude of a simple pendulum is $\omega$ and $A$ respectively. At a displacement $x$ from the mean position, if its kinetic energy is $T$ and potential energy is $U$, then the ratio of $T$ to $U$ is

1 $\left(\frac{\mathrm{A}^{2}-\mathrm{x}^{2} \omega^{2}}{\mathrm{x}^{2} \omega^{2}}\right)$
2 $\left(\frac{x^{2} \omega^{2}}{A^{2}-x^{2} \omega^{2}}\right)$
3 $\frac{\left(A^{2}-x^{2}\right)}{x^{2}}$
4 $\frac{x^{2}}{\left(A^{2}-x^{2}\right)}$
Oscillations

140399 In $\mathrm{SHM}$ restoring force is $\mathrm{F}=-\mathrm{kx}$, where $\mathrm{k}$ is force constant, $x$ is displacement and $A$ is amplitude of motion, then total energy depends upon

1 $\mathrm{k}, \mathrm{A}$ and $\mathrm{m}$
2 $\mathrm{k}, \mathrm{x}, \mathrm{m}$
3 $\mathrm{k}, \mathrm{A}$
4 $\mathrm{k}, \mathrm{x}$
Oscillations

140400 The oscillation of a body on a smooth horizontal surface is represented by the equation,
$X=A \cos (\omega t)$
Where, $X=$ displacement at time $t$
$\omega=\text { frequency of oscillation }$
Which one of the following graphs shows correctly the variation a with $t$ ?

1
2
3
4
Here, $\mathbf{a}=$ acceleration at time $t$
$\mathbf{T}=$ Time period
Oscillations

140401 The total mechanical energy of a harmonic oscillator of $A=1 \mathrm{~m}$ and force constant 200 $\mathrm{Nm}^{-1}$ is $150 \mathrm{~J}$. Then

1 the minimum PE is zero
2 the minimum PE is $100 \mathrm{~J}$
3 the minimum PE is $50 \mathrm{~J}$
4 the maximum $\mathrm{KE}$ is $150 \mathrm{~J}$
Oscillations

140404 A body is executing S.H.M. Its potential energy is $E_{1}$ and $E_{2}$ at displacement $x$ and $y$ respectively. The potential energy at displacement $(x+y)$ is

1 $\mathrm{E}_{1}-\mathrm{E}_{2}=\mathrm{E}$
2 $\sqrt{\mathrm{E}_{1}}-\sqrt{\mathrm{E}_{2}}=\sqrt{\mathrm{E}}$
3 $\mathrm{E}_{1}+\mathrm{E}_{2}=\mathrm{E}$
4 $\sqrt{\mathrm{E}_{1}}+\sqrt{\mathrm{E}_{2}}=\sqrt{\mathrm{E}}$
Oscillations

140398 The angular velocity and the amplitude of a simple pendulum is $\omega$ and $A$ respectively. At a displacement $x$ from the mean position, if its kinetic energy is $T$ and potential energy is $U$, then the ratio of $T$ to $U$ is

1 $\left(\frac{\mathrm{A}^{2}-\mathrm{x}^{2} \omega^{2}}{\mathrm{x}^{2} \omega^{2}}\right)$
2 $\left(\frac{x^{2} \omega^{2}}{A^{2}-x^{2} \omega^{2}}\right)$
3 $\frac{\left(A^{2}-x^{2}\right)}{x^{2}}$
4 $\frac{x^{2}}{\left(A^{2}-x^{2}\right)}$
Oscillations

140399 In $\mathrm{SHM}$ restoring force is $\mathrm{F}=-\mathrm{kx}$, where $\mathrm{k}$ is force constant, $x$ is displacement and $A$ is amplitude of motion, then total energy depends upon

1 $\mathrm{k}, \mathrm{A}$ and $\mathrm{m}$
2 $\mathrm{k}, \mathrm{x}, \mathrm{m}$
3 $\mathrm{k}, \mathrm{A}$
4 $\mathrm{k}, \mathrm{x}$
Oscillations

140400 The oscillation of a body on a smooth horizontal surface is represented by the equation,
$X=A \cos (\omega t)$
Where, $X=$ displacement at time $t$
$\omega=\text { frequency of oscillation }$
Which one of the following graphs shows correctly the variation a with $t$ ?

1
2
3
4
Here, $\mathbf{a}=$ acceleration at time $t$
$\mathbf{T}=$ Time period
Oscillations

140401 The total mechanical energy of a harmonic oscillator of $A=1 \mathrm{~m}$ and force constant 200 $\mathrm{Nm}^{-1}$ is $150 \mathrm{~J}$. Then

1 the minimum PE is zero
2 the minimum PE is $100 \mathrm{~J}$
3 the minimum PE is $50 \mathrm{~J}$
4 the maximum $\mathrm{KE}$ is $150 \mathrm{~J}$
Oscillations

140404 A body is executing S.H.M. Its potential energy is $E_{1}$ and $E_{2}$ at displacement $x$ and $y$ respectively. The potential energy at displacement $(x+y)$ is

1 $\mathrm{E}_{1}-\mathrm{E}_{2}=\mathrm{E}$
2 $\sqrt{\mathrm{E}_{1}}-\sqrt{\mathrm{E}_{2}}=\sqrt{\mathrm{E}}$
3 $\mathrm{E}_{1}+\mathrm{E}_{2}=\mathrm{E}$
4 $\sqrt{\mathrm{E}_{1}}+\sqrt{\mathrm{E}_{2}}=\sqrt{\mathrm{E}}$