A mass at the end of a spring oscillates up and down.  A lab group measures the time for 20 full cycles of oscillation to be 24.0 s.  During an oscillation they also measure the mass to move from a minimum height of 0.0750 m above the benchtop to a maximum height of 0.155 m above the bench top.
What is the period of the oscillation?
 =  s
What is the frequency of the oscillation?
 =  Hz
What is the amplitude of the oscillation?
  =  m

Let's break down each part of the problem:

### 1. **Period of the Oscillation (T):**
The period (\( T \)) is the time it takes for one full oscillation. Since we are given the time for 20 full cycles, the period can be found by dividing the total time by the number of cycles.

\[
T = \frac{\text{Total time for 20 cycles}}{20}
\]

\[
T = \frac{24.0 \, \text{s}}{20} = 1.20 \, \text{s}
\]

### 2. **Frequency of the Oscillation (f):**
The frequency (\( f \)) is the number of cycles per second, which is the inverse of the period.

\[
f = \frac{1}{T}
\]

\[
f = \frac{1}{1.20 \, \text{s}} = 0.833 \, \text{Hz}
\]

### 3. **Amplitude of the Oscillation (A):**
The amplitude is the maximum displacement from the equilibrium position (the midpoint of the motion). Since the mass moves between a minimum height of 0.0750 m and a maximum height of 0.155 m, the amplitude is half the difference between these two values.

\[
A = \frac{\text{Max height} - \text{Min height}}{2}
\]

\[
A = \frac{0.155 \, \text{m} - 0.0750 \, \text{m}}{2} = 0.0400 \, \text{m}
\]

### Final Answers:
- **Period of the oscillation**: \( T = 1.20 \, \text{s} \)
- **Frequency of the oscillation**: \( f = 0.833 \, \text{Hz} \)
- **Amplitude of the oscillation**: \( A = 0.0400 \, \text{m} \)

Would you like more details on any part of this?

Here are 5 related questions to expand your understanding:
1. How would changing the mass affect the period of oscillation in a spring system?
2. What is the relationship between period and angular frequency?
3. How would damping affect the amplitude of the oscillation over time?
4. How can the spring constant be calculated using the oscillation data?
5. What is the potential energy of the mass at the maximum height?

**Tip:** The period of oscillation for a mass-spring system is independent of the amplitude. This means that small or large displacements will have the same period!

A mass at the end of a spring oscillates up and down. A lab group measures the time for 20 full cycles of oscillation to be 24.0 s. During an oscillation they also measure the mass to move from a minimum height of 0.0750 m above the benchtop to a maximum height of 0.155 m above the benchtop. What is the period of the oscillation? = s What is the frequency of the oscillation? = Hz What is the amplitude of the oscillation? = m

Discover how to calculate the period, frequency, and amplitude of a spring oscillation. Given the time for 20 cycles and the mass movement range, this solution walks through the necessary formulas and concepts of simple harmonic motion, perfect for students in Grades 9-11.

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