Q. No.Choose the incorrect statement:
| 1. | All SHM's have a fixed time period. |
| 2. | All motions having the same time period are SHM. |
| 3. | In SHM, the total energy is proportional to the square of the amplitude. |
| 4. | Phase constant of SHM depends on initial conditions. |
| List-I (\(x \text{-}y\) graphs) |
List-II (Situations) |
||
| (a) |  |
(i) | Total mechanical energy is conserved |
| (b) |  |
(ii) | Bob of a pendulum is oscillating under negligible air friction |
| (c) |  |
(iii) | Restoring force of a spring |
| (d) |  |
(iv) | Bob of a pendulum is oscillating along with air friction |
Choose the correct answer from the options given below:
| (a) | (b) | (c) | (d) | |
| 1. | (iv) | (ii) | (iii) | (i) |
| 2. | (iv) | (iii) | (ii) | (i) |
| 3. | (i) | (iv) | (iii) | (ii) |
| 4. | (iii) | (ii) | (i) | (iv) |
During simple harmonic motion of a body, the energy at the extreme position is:
| 1. | both kinetic and potential |
| 2. | is always zero |
| 3. | purely kinetic |
| 4. | purely potential |
Select the correct option based on the statements below:
Particle of mass \(m\) executes SHM along a straight line with an amplitude \(A\) and frequency \(f\).
| Assertion (A): | The kinetic energy of the particle undergoes oscillation with a frequency \(2f\). |
| Reason (R): | This is true because the velocity of the particle, \(v = {\dfrac{dx}{dt}}\) and its kinetic energy equals \({\dfrac 12}mv^2\) and \(v\) oscillates sinusoidally with a frequency \(f\). |
| 1. | Both (A) and (R) are True and the (R) is the correct explanation of the (A). |
| 2. | Both (A) and (R) are True but the (R) is not the correct explanation of the (A). |
| 3. | (A) is True but the (R) is False. |
| 4. | (A) is False but the (R) is True. |
A block is fastened to a spring. The spring has a spring constant of \(50\) N m–1. The block is pulled to a distance \(x = 10\) cm from its equilibrium position at \(x =0\) on a frictionless surface from rest at \(t=0.\) The potential and total energies of the block when it is \(5\) cm away from the mean position respectively are:
| 1. | \(0.0625\) J and \(0.25 \) J | 2. | \(0.625\) J and \(0.25\) J |
| 3. | \(0.0325\) J and \(0.35\) J | 4. | \(0.065\) J and \(3.5 \) J |
| 1. | \(2\sqrt{A}\) | 2. | \(\dfrac{A}{2}\) |
| 3. | \(\dfrac{\mathrm{A}}{\sqrt{2}}\) | 4. | \(A\sqrt{2}\) |
The total mechanical energy of a linear harmonic oscillator is \(600\) J. At the mean position, its potential energy is \(100\) J. The minimum potential energy of the oscillator is:
1. \(50\) J
2. \(500\) J
3. \(0\)
4. \(100\) J
| 1. | \(\sqrt{23}\) m/s | 2. | \(\sqrt{25}\) m/s |
| 3. | \(\sqrt{27}\) m/s | 4. | \(\sqrt{35} \) m/s |
The average energy in one time period in simple harmonic motion is:
1. \(\dfrac{1}{2} m \omega^{2} A^{2}\)
2. \(\dfrac{1}{4} m \omega^{2} A^{2}\)
3. \(m \omega^{2} A^{2}\)
4. zero
A particle executes SHM with time period \(T\). The time period of oscillation of total energy is:
1. \(T\)
2. \(2T\)
3. \(\dfrac{T}{2}\)
4. Infinite
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