Q. No.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
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 spring-mass system oscillates with a frequency \(\nu.\) If it is taken in an elevator slowly accelerating upward, the frequency will:
1. increase
2. decrease
3. remain same
4. become zero
A particle moves in a circular path with a continuously increasing speed. Its motion is:
1. periodic
2. oscillatory
3. simple harmonic
4. none of them
Trains travel between station \(A\) and station \(B\): on the way up (from \(A~\text{to}~B\)) - they travel at a speed of \(80\) km/h, while on the return trip the trains travel at twice that speed. The services are maintained round the clock. Trains leave station \(A\) every \(30\) min for station \(B\) and reach \(B\) in \(2\) hrs. All trains operate continuously, without any rest at \(A\) or \(B\).
| 1. | the frequency of trains leaving \(B\) must be twice as much as \(A\). |
| 2. | the frequency of trains leaving \(B\) must be half as much as \(A\). |
| 3. | the frequency of trains leaving \(B\) is equal to that at \(A\). |
| 4. | the situation is impossible to maintain unless larger number of trains are provided at \(A\). |
The maximum speed and acceleration of a particle undergoing SHM are \(v_0\) and \(a_0,\) respectively. The time period of the SHM is:
1. \(\dfrac{2\pi v_0}{a_0}\)
2. \(\dfrac{2\pi a_0}{v_0}\)
3. \(\dfrac{v_0}{a_0}\)
4. \(\dfrac{2v_0}{a_0}\)
A particle moves in the x-y plane according to the equation
\(x = A \cos^2 \omega t\) and \(y = A \sin^2 \omega t\)
Then, the particle undergoes:
| 1. | uniform motion along the line \(x + y = A\) |
| 2. | uniform circular motion along \(x^2 + y^2 = A^2\) |
| 3. | SHM along the line \(x + y = A\) |
| 4. | SHM along the circle \(x^2 + y^2 = A^2\) |
The time period of a particle in simple harmonic motion is equal to the time between consecutive appearances of the particle at a particular point in its motion. This point is:
| 1. | the mean position |
| 2. | an extreme position |
| 3. | between the mean position and the positive extreme |
| 4. | between the mean position and the negative extreme |
| 1. | uniform circular motion |
| 2. | elliptical motion |
| 3. | linear SHM |
| 4. | angular SHM along a circle |
| 1. | \(8\) | 2. | \(11\) |
| 3. | \(9\) | 4. | \(10\) |
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 |
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