Potential Energy Formulae

Q. The variation of potential energy of a harmonic oscillator is as shown in figure. The spring constant $k$ is

1. $1\times {10}^2\text{N/m}$
2. $1.5\times {10}^2\text{N/m}$
3. $2\times {10}^2\text{N/m}$
4. $3\times {10}^2\text{N/m}$

Q. The potential energy of a spring depends on the displacement 'x' and the spring constant 'K'.

1. False
2. True

Q. The potential energy of the spring increases times, when the elongation of the spring is doubled.

1. two
2. three
3. four

Q. A linear harmonic oscillator of force constant $2\times {10}^6\text{N/m}$ and amplitude $0.01\text{m}$ has a total mechanical energy of $160$ Joules. Which of the following is true?

1. $\text{Maximum potential energy is}100\text{J}$
2. $\text{Maximum K.E. is}160\text{J}$
3. $\text{Maximum P.E. is}160\text{J}$
4. $\text{Minimum P.E. is zero}$

Q. The maximum $\text{K.E.}$ of a oscillating spring is $5\text{J}$ and its amplitude $10\text{cm}$. The force constant of the spring is:

1. $100\text{Newton/m}$
2. $1000\text{Newton-m}$
3. $1000\text{Newton/m}$
4. $1000\text{watts}$

Q. A linear simple harmonic oscillation has a total mechanical energy of $300\text{J}$. Its potential energy at mean position is $100\text{J}$. Find the minimum potential energy.

1. $50\text{J}$
2. $250\text{J}$
3. $100\text{J}$
4. $200\text{J}$

Q. 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 a displacement $(x+y)$ is

(Assume that potential energy at mean position is zero)

1. $E_1+E_2$
2. $\sqrt{E_1^2+E_2^2}$
3. $E_1+E_2+2\sqrt{E_1{E}_2}$
4. $\sqrt{E_1{E}_2}$

Q.

A particle oscillates about the equilibrium position $x_0$ subject to a force that has an associated potential energy U(x). Which of the following statements about U(x) is/are true:

1. u(x) must be symmetric about x${}_0$
2. u(x) must have a minimum at x${}_0$
3. u(x) may have a minimum at x${}_0$
4. u(x) must be positive in the vicinity of x${}_0$

Q. A particle of mass $2\text{kg}$ executes simple harmonic motion and its potential energy $U$ varies with position $x$ as shown below. The period of oscillation of the particle is

1. $\frac{2\pi }{5}\text{s}$
2. $\frac{2\sqrt{2}\pi }{5}\text{s}$
3. $\frac{\sqrt{2}\pi }{5}\text{s}$
4. $\frac{4\pi }{5}\text{s}$

Q. The variation of potential energy of a harmonic oscillator is as shown in figure. The spring constant $k$ is

1. $1\times {10}^2\text{N/m}$
2. $1.5\times {10}^2\text{N/m}$
3. $2\times {10}^2\text{N/m}$
4. $3\times {10}^2\text{N/m}$

Q. The potential energy of a spring depends on the displacement 'x' and the spring constant 'K'.

1. False
2. True

Q. A linear harmonic oscillator of force constant $2\times {10}^6\text{N/m}$ and amplitude $0.01\text{m}$ has a total mechanical energy of $160$ Joules. Which of the following is true?

1. $\text{Maximum potential energy is}100\text{J}$
2. $\text{Maximum K.E. is}160\text{J}$
3. $\text{Maximum P.E. is}160\text{J}$
4. $\text{Minimum P.E. is zero}$