Question

Can someone solve for me this question thanks.

Elastic force:schematization of focce,Calcultion of work.Equation of oscillatory motion with explantion.

Answer 1

Elastic force is directly proportional to -ve of the displacement:-

F∝ -x

=> F=-kx.

(Elastic force schematization)

W.D= Integration of Fdx= integration of -kxdx= -1/2kx^2

F= -kx

=> m•a=-kx

=>m•dv/dt= -kx

=>m•d^2x/dt^2= -kx

=>d^2x/dt^2=-k/m • x

The above eqn is the differential eqn of a simple harmonic eqn whose solution is x= Asin(wt) where w= k/m

And A= amplitude of the oscillation= the extent upto which the elastic material is stretched.