Trains travel between station A and station B: on the way up (from A 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. \(\frac{2\pi v_0}{a_0}\)

2. \(\frac{2\pi a_0}{v_0}\)

3. \(\frac{v_0}{a_0}\)

4. \(\frac{2v_0}{a_0}\)

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:

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

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

The average energy in one time period in simple harmonic motion is:
1. \(\frac{1}{2} m \omega^{2} A^{2}\) 
2. \(\frac{1}{4} m \omega^{2} A^{2}\) 
3. \(m \omega^{2} A^{2}\)
4. zero

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:

During simple harmonic motion of a body, the energy at the extreme position is: