The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and E1 and E2 are the total mechanical energies respectively. Then,

Question

The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and E1 and E2 are the total mechanical energies respectively. Then, (A) E1= √ 2 E2  (B) E1= 2E2  (C) E1= 4E2  (D) E1= 16E2

Tardigrade Admin · Accepted Answer

E= (1/2)m ω2A2 or E propto A2, (E2/E1)= ( (A2/A1) )2= ( (a/2a) )2 or E1=4E2

Q. The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and $E_{1} an d E_{2}$ are the total mechanical energies respectively. Then,

$E_{1} = 2 E_{2}$

$E_{1} = 2 E_{2}$

$E_{1} = 4 E_{2}$

$E_{1} = 16 E_{2}$

$E = \frac{1}{2} m ω^{2} A^{2}$
or $E \propto A^{2},$
$\frac{E _{2}}{E _{1}} = (\frac{A _{2}}{A _{1}})^{2} = (\frac{a}{2 a})^{2}$
or $E_{1} = 4 E_{2}$

Q. The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and E1​andE2​ are the total mechanical energies respectively. Then,

E1​=2​E2​

E1​=2E2​

E1​=4E2​

E1​=16E2​

E=21​mω2A2 or E∝A2, E1​E2​​=(A1​A2​​)2=(2aa​)2 or E1​=4E2​

Q. The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and $E_{1} an d E_{2}$ are the total mechanical energies respectively. Then,

$E_{1} = 2 E_{2}$

$E_{1} = 2 E_{2}$

$E_{1} = 4 E_{2}$

$E_{1} = 16 E_{2}$

$E = \frac{1}{2} m ω^{2} A^{2}$
or $E \propto A^{2},$
$\frac{E _{2}}{E _{1}} = (\frac{A _{2}}{A _{1}})^{2} = (\frac{a}{2 a})^{2}$
or $E_{1} = 4 E_{2}$