Answer:19.5 J
Explanation:
Given
mass of block=3 kg
angular frequency=20 rad/sec
spring constant [tex]k=\omega _n^2m=1200 N/m[/tex]
we know total energy remain conserved
[tex]E_T at x=0.1 m[/tex]
[tex]E_T=E_P+E_K[/tex]
Where [tex]E_K[/tex]=kinetic energy
[tex]E_P[/tex]=potential Energy
[tex]E_P=\frac{1}{2}kx^2[/tex]
[tex]E_P=600\times 0.01=6 J[/tex]
[tex]E_K=\frac{1}{2}mv^2[/tex]
[tex]E_K=\frac{1}{2}\times 3\times 3^2=13.5 J[/tex]
[tex]E_T=13.5+6=19.5 J[/tex]
When mass reaches amplitude its velocity becomes zero
there is only potential energy which is equal to Total energy
[tex]E_T=E_P=19.5 J[/tex]
