The phase space diagram for harmonic motion is a circle centered at the origin as shown in figure. The to circles represent the same oscillator but for different initial conditions and `E_(1)` and `E_(2)` are the total mechanical energy, respectively . Then

Options

A. `E_(1)=sqrt(2)E_(2)`
B. `E_(1)=2E_(2)`
C. `E_(1)=4E_(2)`
D. `E_(1)=16E_(2)`

Answer

C

Explanation

For a simple harmonic oscillator, `E=(1)/(2)kA^(2)`
where A is the amplitude and K is a force constant.
Both oscillators have the same K.
`therefore E_(1) =(1)/(2)K(2a)^(2) and E_(2)=(1)/(2)K(a)^(2)`
` therefore (E_(1))/(E_(2))=(4a^(2))/(a^(2))=4 therefore E_(1)=4E_(2)`