A body of mass M is released from a height h to a scale pan hung from a spring as shown in fig (9). The spring
constant of the spring is k, the mass of the scale pan is negligible and the body does not bounce relative to the pan, then the amplitude of vibration is

Question

A body of mass M is released from a height h to a scale pan hung from a spring as shown in fig (9). The spring

constant of the spring is k, the mass of the scale pan is negligible and the body does not bounce relative to the pan, then the amplitude of vibration is

Infinity Learn · Accepted Answer

Let y be the displacement of the pan when the mass m hits it. Decrease in potential energy of mass $$=mg(h+y)$$,$$y=$$ amplitude. Increase in elastic potential energy of $$spring=12ky2$$ ∴ $$mg(h+y)=12ky2$$ or $$y2$$−$$2mgry$$−$$2mghk=0$$ $$y2$$−$$2mgry$$−$$2mghk=0$$ $$y=(2mg/k)$$±$$(2mg/k)2+4(2mgh/k)2$$ Reiecting negative sign, the total extension is $$y=mgk+mgk1+2hkmg$$ $$=mgk1+1+2hkmg$$

A body of mass M is released from a height h to a scale pan hung from a spring as shown in fig (9). The spring
constant of the spring is k, the mass of the scale pan is negligible and the body does not bounce relative to the pan, then the amplitude of vibration is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material