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How come this is possible???

but the following integral is ugly:

What's The Hell Is Going On With Integrals?

How come this is possible???

but the following integral is ugly:

Due in
2 months, 2 weeks
Posted 1 month ago by fluidistic
Earn
19
Credits

A fly follows a trajectory given in polar coordinates as $$r(t)= cos^2\left(\frac{t}{\alpha}\right)$$ where the polar angle $$\theta=t/\alpha$$ is dependent on time $$t$$. What is the least speed the fly can achieve?

A Fly's Speed

A fly follows a trajectory given in polar coordinates as $$r(t)= cos^2\left(\frac{t}{\alpha}\right)$$ where the polar angle $$\theta=t/\alpha$$ is dependent on time $$t$$. What is the least speed the fly can achieve?

Due in
2 weeks, 4 days
Posted 1 week, 4 days ago by Victor
Earn
7
Credits

A critically damped harmonic oscillator satisfies the equation $$\\ddot{x}+10\dot{x}+25x=0$$ At time $$t=0$$, the particle is at x=1 with speed $$v$$. Find $$x$$ in the subsequent motion

Harmonic Oscillator

A critically damped harmonic oscillator satisfies the equation $$\\ddot{x}+10\dot{x}+25x=0$$ At time $$t=0$$, the particle is at x=1 with speed $$v$$. Find $$x$$ in the subsequent motion

Due in
2 weeks, 4 days
Posted 1 week, 4 days ago by RedCrab
Earn
19
Credits

How is the quantum mechanical notion of position $$x$$ expressed in momentum representa- tion?

Position In Momentum Representation

How is the quantum mechanical notion of position $$x$$ expressed in momentum representa- tion?

Due in
2 weeks, 4 days
Posted 1 week, 4 days ago by Blondy
Earn
9
Credits

Evaluate the following commutation relations $$a) \left[\hat{x},\hat{p}\right]$$ $$b) \left[\hat{x}^2,\hat{T}\right]$$ $$c) \left[\hat{p}^2,\hat{T}\right]$$ where $$\hat{x}$$ is the position operator, $$\hat{p}$$ the momentum operator and $$\hat{T}$$ the kinetic energy operator.

Commutation Relation

Evaluate the following commutation relations $$a) \left[\hat{x},\hat{p}\right]$$ $$b) \left[\hat{x}^2,\hat{T}\right]$$ $$c) \left[\hat{p}^2,\hat{T}\right]$$ where $$\hat{x}$$ is the position operator, $$\hat{p}$$ the momentum operator and $$\hat{T}$$ the kinetic energy operator.

Due in
2 weeks, 4 days
Posted 1 week, 4 days ago by Alex
Earn
20
Credits

Find the angle at which a projectile, fired from ground with speed $$100 m/s$$, must be thrown to land on a final height, $$10 m$$ units above the ground and at a range $$100 m$$ from the initial position. Calculate the time of flight.

Projectile Motion

Find the angle at which a projectile, fired from ground with speed $$100 m/s$$, must be thrown to land on a final height, $$10 m$$ units above the ground and at a range $$100 m$$ from the initial position. Calculate the time of flight.

Due in
2 weeks, 4 days
Posted 1 week, 4 days ago by Victor
Earn
16
Credits

Find the potential inside and outside a spherical surface of radius $$R$$ which carries a surface charge density $$\sigma$$ on the northern hermisphere and $$-\sigma$$ on the southern hermisphere.

Electric Potential

Find the potential inside and outside a spherical surface of radius $$R$$ which carries a surface charge density $$\sigma$$ on the northern hermisphere and $$-\sigma$$ on the southern hermisphere.

Due in
2 weeks, 4 days
Posted 1 week, 4 days ago by Lexus
Earn
8
Credits

Find the solution for a free particle initially localized at $$-\frac{b}{2} < x < \frac{b}{2}$$ then released at time $$t=0$$. $$\Psi(x,0)=\left\{\begin{array} &B\;\;\;\;\;-\frac{b}{2} < x < \frac{b}{2} \\ &0\;\;\;\;\;otherwise \end{array}\right.$$

Wave Function

Find the solution for a free particle initially localized at $$-\frac{b}{2} < x < \frac{b}{2}$$ then released at time $$t=0$$. $$\Psi(x,0)=\left\{\begin{array} &B\;\;\;\;\;-\frac{b}{2} < x < \frac{b}{2} \\ &0\;\;\;\;\;otherwise \end{array}\right.$$

Due in
2 weeks, 4 days
Posted 1 week, 4 days ago by Googler
Earn
18
Credits

Find the maximum increase in photon wavelength that can occur during Compton scat- tering.

Compton Scattering

Find the maximum increase in photon wavelength that can occur during Compton scat- tering.

Due in
2 weeks, 3 days
Posted 1 week, 4 days ago by Lexus
Earn
15
Credits

A twirler's baton is made up of a metal rod of length $$l$$ and two rubber spheres, each of radius $$r$$, connected to the ends of the rod. Determine the moment of inertia if the baton is rotated at an axis i) about the center of mass of the baton; ii) about the center of one sphere. Which of these two axes of rotation gives the greatest angular speed?

A twirler's baton is made up of a metal rod of length $$l$$ and two rubber spheres, each of radius $$r$$, connected to the ends of the rod. Determine the moment of inertia if the baton is rotated at an axis i) about the center of mass of the ...