1. Chapter 11-2 Measuring Simple Harmonic Motion
St. Augustine Preparatory School
March 31, 2016

2. Definitions
Amplitude: The maximum displacement from equilibrium (meters or radians)
Period: The time that it takes a complete cycle to occur (unit: seconds)
Frequency: The number of cycles or vibrations per unit time (unit: Hertz (s-1) )

3. The period of a pendulum depends on which factors?

4. The period of a pendulum depends on which factors?
Pendulum Length and Free Fall Acceleration (gravity)

5. Period of a Simple Pendulum in Simple Harmonic Motion
Formula:
Period = 2*pi*square root of (length/acceleration of gravity)
T: Period (unit: s)
2π: 2*3.14 (unitless)
L = length (unit: m)
ag = acceleration of gravity (unit: m/s2) Use 9.81 m/s2 on Earth

6. Nevis Swing – New Zealand!
(start at 2:20)

7. Example 1 – Nevis Swing
Queenstown, New Zealand is the home of the World’s Largest Swing. Here, you are connected to a 120. m long rope (a soccer field is 110. m long) which makes an arc with a distance of 300 m. The site claims you travel at a speed of 120 km/h on this swing. Does this claim seem reasonable? Why or why not? (This will require us to think about a few different things).

8. Example 2
You jump off of a platform with a rope around feet and end up in a parabolic path, like a pendulum. If your period for one cycle is 12 s, how high above the ground is the platform you are swinging from?

9. Solution

10. Frequency The formula for frequency is:
Frequency is equal to 1 divided by the period
f = frequency (unit: Hz)
T = period (unit: s)

11. Period for Mass Spring Systems
The period of a mass spring system depends on:
Mass
Spring Constant
Why does mass matter now when it didn’t in the pendulum system?

12. Increasing the mass of an object increases the inertia (resistance to movement) of that object . In a pendulum, increasing the mass also increases the Fg on the object, so the increase in mass is compensated for. In a spring system it does not add any extra force, so the mass does matter.

13. Period for Mass Spring Systems in SHM
𝑇=2𝜋 𝑚 𝑘 Period = 2*pi*sqrt(mass divided by spring constant) Period – seconds (s) Mass – kilograms (kg) Spring Constant – Newtons per meter (N/m)

14. Practice Problem
The body of a 1275 kg car is supported on a frame by four springs. Two people riding in the car have a combine mass of 153 kg. When driven over a pothole in the road, the frame vibrates with a period of s. For the first few seconds, the vibration approximates simple harmonic motion. Find the spring constant of a single spring.

15. Solution

16. Graded Problems
A 125 N object vibrates with a period of 3.56 s when hanging from a spring. What is the spring constant of the spring?
You are designing a pendulum clock to have a period of 1.0 s. How long should the pendulum be?
A trapeze artist swings in simple harmonic motion with a period of 3.8 s. Calculate the length of the cables supporting the trapeze.
Calculate the period and frequency of a m long pendulum at Jakarta, Indonesia, where the acceleration from gravity is m/s2.