A body is dropped on to the floor from a height h. It makes elastic collision with the floor bouncing back to the same height. The frequency of oscillation of its periodic motion is

Question

A body is dropped on to the floor from a height h. It makes elastic collision with the  floor bouncing back to the same height. The frequency of oscillation of its periodic  motion is

Infinity Learn · Accepted Answer

The body of mass m is at rest on top. It undergoes free fall and attains a speed of  $$v1$$ at the bottom.According to the law of conservation of energy, $$mgh$$$$=12mv12$$ .On simplifying this we get  $$v1=2gh$$…………..$$(1)Using$$ this we find the time taken to go down the inclined plane using equations of  motion.$$v=u+at$$  , Substituting $$v=2gh$$ ,   $$u=0$$ and $$a=g$$ ,We get $$2gh=u+g$$ t ,Therefore, $$2ghg$$ $$=t$$ .This is time of descent. The total time taken to complete one full oscillation will be  two times the time taken to reach the ground.Hence  $$22ghg$$ $$=Ti$$.e.  $$T=22hg$$ and  $$f=12g2h$$

A body is dropped on to the floor from a height h. It makes elastic collision with the floor bouncing back to the same height. The frequency of oscillation of its periodic motion is

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