Recent content by Luke1121

Homework Statement How to calculate the matrix elements of the quantum harmonic oscillator Hamiltonian with perturbation to potential of -2cos(\pi x) The attempt at a solution H=H_o +H' so H=\frac{p^2}{2m}+\frac{1}{2} m \omega x^2-2cos(\pi x) I know how to find the matrix of the normal...

Homework Statement A pendulum has a length of 0.5m and an amplitude of oscillation of 8 degrees, what is maximum vertical acceleration Homework Equations X=Acos(\omega t + \phi) \omega =\frac{2\pi}{T} T=2\pi \sqrt{\frac{l}{g}}The Attempt at a Solution Taking the second derivative with respect...

Ah ok, so: Tcos\theta=mg (1) Tsin\theta=m\omega^2R (2) doing (2)/(1) gives R=\frac{gtan\theta}{\omega^2} plugging in the numbers gives 0.036m, is this correct?

Homework Statement A pendulum is placed on a rotating platform which rotates with angular velocity ω around an axis, at equilibrium the angle between vertical and pendulum is θ θ= 20 degrees ω= 10 1/s how far is the pendulum placed from the axis Homework Equations...

Ok, then doing the indefinite integral gives v=\sqrt{\frac{2GM}{x}} + C but I'm not sure about the limits, would it be \frac{1}{2}v^2=-GM\int_{\infty}^{6370}x^{-2} where 6370 is the radius of the Earth in km? Thanks

Homework Statement Assuming the Earth is at rest and alone in the universe what speed would a spaceship arriving at the surface of Earth from an infinitley large distance be if the speed at infinity= 0 and acceleration is caused only by gravity Homework Equations F= \frac{GmM}{x^2}...

I've got an answer to a question but I'm not sure if it's correct as i don't have the answers. A roller coaster train is propelled at 57m/s and towards a vertical part of track which has a height of 139m, what is the velocity of the roller coaster train when it reaches the top of the tower...

Thanks for that, it seems I overcomplicated things, i feel silly for not knowing something so simple

I was asked a relativley simple question by someone the other day and I was a little shocked that I didn't know. The question was why is it harder to open a car door when it's at an angle parked half on the pavement and half on the road. I had a go at answering the person but I have no idea if...

Ah of course it's not -m, seems like I confused myself. Thank you

If I=s/4pir2 would It be correct to write this in terms of logs like this:. lnI=(lns/4pi)-2.lnr Also how could this relate to y=mx+c? I think it's y=lnI. X=lnr. -m= -2 and c= lns/4pi. Is this correct? Thank you

I was doing a past paper earlier and i got a question about cold spots in microwaves and i needed to calculate path difference the question was: ---------|------->S<---------|--------- Explain why a cold spot is formed at S 18cm | 6cm. 12cm | 30cm The question showed the...

When plotting a stress against strain graph is this the right equation that fits the form y=mx+c? I got (F/A)=y(dL/L) where F is force A is area y is youngs modulus dL is change in length and L is original length. The Y is F/A. The m is y and x is dL/l (in y=mx) is this correct? Thank you

I've just finished some past exam papers and when marking them using the mark scheme something confused me a little One question said when a fire engine moves away from an observer, the pitch of the siren decreased, why and I chose the wavelength of the sound wave decreases The mark scheme...