AP Physics 1- 7.2 Frequency and Period of SHM- Study Notes- New Syllabus
AP Physics 1-7.2 Frequency and Period of SHM – Study Notes
AP Physics 1-7.2 Frequency and Period of SHM – Study Notes -AP Physics 1 – per latest Syllabus.
Key Concepts:
- Frequency and Period of SHM
Frequency and Period of SHM
- Time Period (T): The time taken by an object to complete one full oscillation is called the time period.
- Frequency (f): The number of complete oscillations made by the object in one second is called the frequency.
Relationship between Frequency and Time Period:
\( f = \dfrac{1}{T} \quad \text{or} \quad T = \dfrac{1}{f} \)
SHM Specific Formulas:
For a mass-spring system:
\( T = 2 \pi \sqrt{\dfrac{m}{k}} \), \( f = \dfrac{1}{2 \pi} \sqrt{\dfrac{k}{m}} \)
For a simple pendulum (small angles):
\( T = 2 \pi \sqrt{\dfrac{L}{g}} \), \( f = \dfrac{1}{2 \pi} \sqrt{\dfrac{g}{L}} \)
Key Points:
- Time period and frequency are independent of amplitude for ideal SHM.
- Time period depends on the mass and spring constant for a spring system, and length and gravity for a pendulum.
- Frequency is the reciprocal of time period and indicates how fast the oscillations occur.
Example:
A 0.25 kg mass is attached to a spring with force constant \( k = 100 \, \text{N/m} \). Find the frequency and time period of oscillation.
▶️Answer/Explanation
Time period: \( T = 2 \pi \sqrt{\dfrac{m}{k}} = 2 \pi \sqrt{\dfrac{0.25}{100}} \approx 0.314 \, \text{s} \)
Frequency: \( f = \dfrac{1}{T} \approx \dfrac{1}{0.314} \approx 3.18 \, \text{Hz} \)
Answer: \( T \approx 0.314 \, \text{s}, \ f \approx 3.18 \, \text{Hz} \)
Example :
A simple pendulum of length \( L = 0.8 \, \text{m} \) is oscillating near the Earth’s surface. Find its time period and frequency. (Take \( g = 9.8 \, \text{m/s}^2 \))
▶️Answer/Explanation
Time period: \( T = 2 \pi \sqrt{\dfrac{L}{g}} = 2 \pi \sqrt{\dfrac{0.8}{9.8}} \approx 1.79 \, \text{s} \)
Frequency: \( f = \dfrac{1}{T} \approx \dfrac{1}{1.79} \approx 0.56 \, \text{Hz} \)
Answer: \( T \approx 1.79 \, \text{s}, \ f \approx 0.56 \, \text{Hz} \)