# Week 18

**Reading:**PSE Chap 13 ( Simple harmonic motion) and 16, waves

**Some fascinating resources:**

- The loudest sound in recent history occurred when Krakatoa erupted on August 27, 1883. Check out this article from Nautilus magazine: The sound so loud that it circled the earth four times. For a more technical report, here is VerBeeks' 1884 paper in Nature magazine detailing the Krakatoa eruption. VerBeek, R.
*The Krakatoa Eruption*. Nature**30**, 10–15 (1884). - This video documentary of the December 2019 volcanic eruption on White Island has disturbing accounts from survivors who were trapped on the island.
- The pressure wave created by the explosion of a volcano of Papua New Guinea was documented in this video.
- On a different note, Wikipedia has a nice article on the famous Tunguska event of 1908, when a meteor struck in central Russia.
- And of course, there is the eruption of Mount St. Helens on May 18, 1980.

**Just for practice for the final exam on Friday, Dec. 23.**

Homework Problems:

Homework Problems:

**Ice cube:**A large ice cube, whose density is 0.917 g/cc, is placed in a glass. Water is then poured into the glass until the glass is full to the rim.- First, what fraction of the ice cube is submerged? (Solution: 91.7 percent)
- When the ice melts, will the water level overflow the glass, will it fall below the rim, or will it remain the same? Explain your answer. (Solution: it would remain at the same level. Suppose the ice cube had a volume of 1 cc. 0.917 cc was below water. When it melts, the new volume will be 0.917 cc, since its density increased by just this much.)
**Hydraulics:**A fluid-filled syringe has a plunger with a diameter of 1 cm. The needle has a diameter of 1 mm. The plunger is depressed at a rate of 1 cm per second.- With what speed will the fluid squirt from the tip of the needle? (Since the cross-sectional area of the needle is 1/100 that of the plunger, the speed will be 100 times as great. So the fluid squirts out at 100 cm/second.)
- If the end of the needle is capped, and a force of 1 pound is applied to the plunger, what force will be applied to the end cap? Explain your answer. (By pascal's principle, the force will be 1/100 of a pound)
**Mass on a spring:**A block of mass M = 1 kg is placed on a frictionless table. It is attached to a spring whose spring constant is 5 N/meter. The spring is compressed by 5 cm and then released at time t = 0.- What is the angular frequency of the mass as it oscillates back and forth across the surface of the table? (omega = sqrt(5) rad/sec)
- Write down a mathematical function that describes the motion of the mass as a function of time. (x = 5cm * cos(omega * t))
- Make a plot of this function and label your axes appropriately.
- What are the kinetic energy and potential energies of the mass-spring system at t = 1 second.
- Wha tis the total energy of the mass-spring system while it is oscillating? (E = 2/160 joules)