Explanation
Kinetic energy varies with time but is never negative
Motion given here is S.H.M. starting from rest.
The period of the liquid executing S.H.M. in a U-tube does not depend upon the density of the liquid. Therefore, time period will be the same, when mercury is filled up to the same height as the water in the U-tube.
Now, as the pendulum oscillates, it drags air along with
it. Therefore, its kinetic energy is dissipated in overcoming viscous drag due to air and hence, its amplitude goes on decreasing.
In S.H.M. the acceleration is always in a direction opposite to that of the displacement i.e., proportional to (–y).
Waves produced on the surface of water arc transverse in nature. When such waves are produced in water they spread out. Till the ocean waves reach the beach-shore, they acquire such a large radius of curvature that they may be assumed as plane waves.
Hence, ocean waves hit the beach normal to the shore.
If the soldiers while crossing a suspended bridge march in steps, the frequency of marching steps of soldiers may match with the natural frequency of oscillations of the suspended bridge. In that situation resonance will take place, then the amplitude of oscillation of the suspended bridge will increase enormously, which may cause the collapsing of the bridge. To avoid such situations the soldiers are advised to break steps on suspended bridge.
Time period of pendulum doesn’t depends upon mass but it depends upon length (distance between point of suspension and centre of mass).
In first three cases length are same so T = T1 = T2 but in last case centre of mass lowers which in turn increases the length. So in this case time period will be more than the other cases.
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