General Questions
- I want you to test the applet "spring" which can be found at spring applet
In particular I want you to assess:
- whether or not it provides a correct period (or frequency) for any given set of mass and spring constants
- whether or not it provides accurate graphical output of such things as x-t and v-t.
Choose 5 combinations of mass and spring constant to do this and compare what the applet states with what you calculated by hand.
- Use EXCEL to investigate the equation for a travelling wave. Specifically, prepare a graph in which you show the wave y = 2.5sin(4x-5t) between x = -4m and x = +4 m and for times t = 0, 0.25, 0.50, 0.75 and 1.0 s. Explain how your graph shows that this wave really is moving, also identifying the direction in which it is moving and how fast the wave is moving.
- A spring of mass 1g and k = 10 N/m is attached to a 400g mass which is then pulled 10 cm away from equilibrium. If the mass is released at time t = 0s determine its position, velocity and acceleration at time t = 2.1 s. You may ignore friction and any other possible damping effects on the spring-mass system. Use Excel to prepare a graph showing the kinetic and potential energy in the system over the 2.1 s in question.
- A clever entrepreneur has created an "elevator by tunneling through the earth! To send a package to the other side of the earth you simply drop it down the hole! How long does it take for the package to emerge from the hole? Show that:
- this is an example of SHM
- the period is comparable (but not the same as) the orbital period of a satellite travelling around the earth in a circular orbit of radius R
