Problem 1
A weight of mass  g hangs on a stick. The weight is pushed up and down by a motor. The position of the weight is given by,

Here $t$ is the time in seconds and $\varphi$ is the phase.

When the angular frequency is $\omega = 100$ rad/s, what is the maximum force on the weight?

$F_{\text{max}} = $ [N]

Problem 2
A weight with a mass of 100 g hangs motionless from a spring at $y=0$ m. The spring constant is $k=$  N/m.

At $t=0$, the weight is given a push so that its position and velocity are:   $y(t=0)=0$ m,  $v_y(t=0)=-1$  m/s.

There is a damping force directed opposite to the velocity, $\vec{F}_{fric}= -0.1\left|\frac{d\vec{y}}{dt}\right|\frac{d\vec{y}}{dt}$ N.

Where is the weight at time $t =$  s?

This problem must be solved numerically.

Problem 3
A long straight wire lies on the $z$-axis of a coordinate system. An electric current of  mA flows through this wire in the positive $z$-direction. An electron moves by this wire. When the electron is at position,

$\vec{r}= 0\hat{x}+0.01\hat{y}+0\hat{z}$ [m]

its velocity is,

$\vec{v}=$$\hat{x}$ + $\hat{y}$ - $\hat{z}$ [m/s].

What is the Lorentz force on this electron?

Electron mass = $9.10938356 \times 10^{-31}$ kg  Electron charge = $-1.6021766208 \times 10^{-19}$ C

Problem 4

Water waves propagate away from a point source at ($x=$  m, $y=$  m). The speed of the waves is  m/s and the wavelength is  m. At $(x=0,\,y=0)$ the maximum height of the waves is $z=$  cm and the minimum height of the waves is $z=$  cm.

Give a formula that describes these waves.

Problem 5
In a double slit experiment, light with a wavelength of $\lambda = 780$ nm passes through two narrow slits that are separated by a spacing $d$. The interference pattern shown below is observed on a screen that is 1 meter from the slits.

What is the distance between the slits? The small divisions on the scale on the right represent mm.

Problem 6

An object is placed at a distance $x_o$ cm to the left of a converging lens. The lens has a focal length of  cm.

A sharp image of the object appears on a screen that is  cm to the right of the lens.

How far is the object from the lens? $x_o=$  cm

What is the magnification of the image?   $m=$