The curve between the potential energy \((U)\) and displacement \((x)\) is shown. Which of the oscillation is about the mean position, \(x = 0?\)
1. | 2. | ||
3. | 4. |
A particle of mass m oscillates with simple harmonic motion between points x1 and x2, the equilibrium position being O. Its potential energy is plotted. It will be as given below in the graph:
1. | 2. | ||
3. | 4. |
Equation of a simple harmonic motion is given by x = asint. For which value of x, kinetic energy is equal to the potential energy?
1.
2.
3.
4.
When the displacement is half the amplitude in an SHM, the ratio of potential energy to the total energy is:
1. 1 / 2
2. 1 / 4
3. 1
4. 1 / 8
The potential energy of a simple harmonic oscillator, when the particle is halfway to its endpoint, will be:
1. \(\frac{2E}{3}\)
2. \(\frac{E}{8}\)
3. \(\frac{E}{4}\)
4. \(\frac{E}{2}\)
The kinetic energy (K) of a simple harmonic oscillator varies with displacement (x) as shown. The period of the oscillation will be: (mass of oscillator is 1 kg)
1. | sec | 2. | sec |
3. | sec | 4. | 1 sec |
A block of mass \(4~\text{kg}\) hangs from a spring of spring constant \(k = 400~\text{N/m}\). The block is pulled down through \(15~\text{cm}\) below the equilibrium position and released. What is its kinetic energy when the block is \(10~\text{cm}\) below the equilibrium position? [Ignore gravity]
1. \(5~\text{J}\)
2. \(2.5~\text{J}\)
3. \(1~\text{J}\)
4. \(1.9~\text{J}\)
Kinetic energy of a particle executing simple harmonic motion in straight line is \(pv^2\) and potential energy is \(qx^2,\) where \(v\) is speed at distance \(x\) from the mean position. The time period of the SHM is given by the expression:
1.
2.
3.
4.
The total energy of a particle, executing simple harmonic motion is:
1.
2.
3. Independent of x
4.
A particle executes SHM with a frequency of \(20\) Hz. The frequency with which its potential energy oscillates is:
1. \(5\) Hz
2. \(20\) Hz
3. \(10\) Hz
4. \(40\) Hz