Important conceptual questions of periodic motion class 12

Check out the important conceptual questions of periodic motion.

1. The girl sitting on a swing stands up. What will be the effect on the periodic time of the swing?
   Ans: The time period T will decrease because on the standing position, the centre of mass of the girl shifts upwards. Due to which the effective length of the pendulum l becomes smaller. As T = 2π \(\mathsf{\sqrt{\frac{l}{g}}}\), so T decreases.
2. A man with a wrist watch on his hand falls from the top of a tower Does the watch give correct time during the free fall?
   Ans: Yes, because the working of the wrist watch depends on spring action and it has nothing to do with gravity.
3. What is the frequency of oscillation of a simple pendulum mounted in a cabin that is freely under gravity?
   Ans: Since, frequency, f = \(\mathsf{\frac{1}{2π}}\)\(\mathsf{\sqrt{\frac{g}{l}}}\), the value of g inside the freely falling cabin is zero. So, frequency is zero and the time period is infinity.
4. Is the motion of a simple pendulum strictly simple harmonic?
   Ans: It is not strictly simple harmonic because we make the assumption that sinθ = θ which is nearly valid only if θ is very small. Viscosity of air reduces the amplitude also.
5. How does the displacement and velocity of a body executing SHM vary?
   Ans: At the point where displacement is zero (mean position); the velocity of a body executing SHM is maximum and vice versa.
6. What is the most important characteristic of simple harmonic motion?
   Ans: The most important characteristic of SHM is that acceleration is directly proportional to the displacement and is directed opposite to the displacement. Mathematically, a = -ω\(\mathsf{^{2}}\)r.
7. Why does the motion of simple pendulum eventually stop?
   Ans: The energy of the simple pendulum is converted into heat energy due to the frictional force of the medium i.e. air. So, the energy of the simple pendulum decreases slowly and ultimately, the oscillating simple pendulum comes to rest.
8. The rotation of the earth about its axis is periodic but not simple harmonic. Justify.
   Ans: The earth takes 24 hours to complete it's rotation about its axis, but the concept of to and fro motion is absent, and hence the rotation of the earth is periodic and not simple harmonic.
9. When are the displacement and velocity in the same direction in SHM?
   Ans: When a particle moves from mean position to extreme position,it's displacement and velocity are in the same direction.
10. How can earthquake cause disasters sometimes?
    Ans: The resonance may cause disaster during the earthquake, if the frequency of oscillation present within the earth coincides with the natural frequency of some buildings, they may start vibrating with large amplitudes due to resonance and may get damaged.
11. What will be the change in time period of a loaded spring, when taken to moon?
    Ans:Time period of a loaded spring is given by,
    T = 2π\(\mathsf{\sqrt{\frac{m}{k}}}\)
    As T is independent of g, it will not be affected when the loaded spring is taken to the moon.