Question

I need the solution for question number 24

Answer 1

The time period of Simple harmonic motion SHM of the mass spring system will be option 1) 2 π/3 √(m/k)

   Assume that the elastic wall does not exist. The situation will be identical to the case when the wall is there. The difference is that with the wall, only a part of the SHM is executed between x = - 2e and x = -e positions. A full SHM would be between positions   x = -2e, to x = -e, x = 0, x = e, to x = +2e.

Let the equation of motion be  x = 2e Sin(3π/2 + 2π t/T).
    So at t = 0, x = - 2e, as per given condition.
    Let  at  t = t1, x = - e.

Here, T is the time period of SHM when there is no wall. Thus
      T = 2 π √(m/k)

   so    -e = 2 e Sin (3π/2 + 2π t1 /T) 
          - 1/2 = Sin (11π/6) = Sin (3π/2 + 2 π t1 / T)
           2π t1 / T = π/3
           t1 = π/3 √(m/k) 
 
The time period in the given situation is equal to  = 2 * t1 
        = 2 π/3 * √(m/k)

This because from position x = -e the mass will rebound at the same speed due to elastic wall.

Answer 2

The Indian Atomic Energy Commission (AEC) is the main policy body. The Nuclear Power Corporation of India Ltd (NPCIL) is responsible for design, construction, commissioning and operation of thermal nuclear power plants. At the start of 2010 it said it had enough cash on hand for 10,000 MWe of new plant.