Answer:
Explanation:
Given
mass of block is M
Force constant is k
Natural Frequency of oscillation [tex]\omega _n=\sqrt{\frac{k}{m}}[/tex]
Potential Energy at any instant [tex]U=\frac{1}{2}kx^2[/tex]
where x is compression in spring
[tex]U=\frac{1}{2}k(\frac{A}{4})^2[/tex]
[tex]U=\frac{1}{2}k(\frac{A}{16})[/tex]
Total Energy [tex]=\frac{1}{2}kA^2[/tex] when mass is at maximum Position
Total Energy=Kinetic Energy+Potential Energy
kinetic Energy[tex]=\frac{1}{2}kA^2-\frac{1}{32}kA^2[/tex]
Kinetic Energy[tex]=\frac{15}{32}kA^2[/tex]
(b)If one adds a mass smoothly in a vertical drop at [tex]x=A[/tex]
then its amplitude is going to decrease because more mass is added to the system
its natural frequency changed to [tex]\omega _n' =\sqrt{\frac{k}{2M}}[/tex]
so time Period increases because [tex]T\cdot \omega =2\pi [/tex]
[tex]T=\frac{2\pi }{\omega _n'}[/tex]
