Thanks, i thought this could be the case. Then inside the square brackets I am assuming we can rearrange the second term so that the first and second term are the same. so we get 1/2*[...] + 1/2*[...] = [...]. and this [...] cancels with the second term of the whole line, resulting in line (32)?
Im studying Quantum Field Theory as part of my undergraduate course, and am currently looking at Noether's Theorem which has led me to the following calculation of the divergence of the Stress-Energy Tensor. I'm having difficulty in seeing how we get from line (31) to line (32). Is the 2nd term...
the damped oscillator equation:
(m)y''(t) + (v)y'(t) +(k)y(t)=0
Show that the energy of the system given by
E=(1/2)mx'² + (1/2)kx²
satisfies:
dE/dt = -mvx'
i have gone through this several time simply differentiating the expression for E wrt and i end up with
dE/dt =...
the damped oscillator equation:
(m)y''(t) + (v)y'(t) +(k)y(t)=0
Show that the energy of the system given by
E=(1/2)mx'² + (1/2)kx²
satisfies:
dE/dt = -mvx'
i have gone through this several time simply differentiating the expression for E wrt and i end up with
dE/dt =...
hi cosmic dust, thanks for your reply!
so by taking the derivative wrt time of the energy expression, i get
dE/dt = s' s'' + s'(ω^2s^2)
which is just s' times the given oscillator equation, which is zero, so:
dE/dt = s'(0)=0
So basically, by showing dE/dt = 0, i have shown that energy is...
Given the Oscillator equation:
\frac{d2s}{dt2} + \omega2s = 0
Show that the energy:
E=1/2(\frac{ds}{dt})2 + 1/2\omega2s2
is conserved.
Any help at all appreciated! Thankyou