To solve this problem, we will use the relationship between the period of oscillation in simple harmonic motion, the spring constant, and the mass of the object.

Step 1: Find the period of oscillation

The total time for 14 oscillations is $t = 16 \, \text{s}$. Therefore, the period of one oscillation, $T$, is:

$T = \frac{\text{Total time}}{\text{Number of oscillations}} = \frac{16}{14} \approx 1.14 \, \text{s}$

Step 2: Use the formula for the period of a spring-mass system

The period of oscillation for a spring-mass system is given by:

$T = 2\pi \sqrt{\frac{m}{k}}$

Where:

• $T$ is the period ($1.14 \, \text{s}$),
• $k$ is the spring constant ($220 \, \text{N/m}$),
• $m$ is the mass of the object.

Rearranging the formula to solve for $m$:

$m = \frac{T^2 k}{4\pi^2}$

Step 3: Substitute the known values

Substitute $T = 1.14 \, \text{s}$ and $k = 220 \, \text{N/m}$:

$m = \frac{(1.14)^2 \cdot 220}{4\pi^2}$

Step 4: Calculate $m$

First, calculate $1.14^2$:

$1.14^2 = 1.2996$

Now substitute into the equation:

$m = \frac{1.2996 \cdot 220}{4\pi^2}$

$m = \frac{285.912}{39.4784} \approx 7.24 \, \text{kg}$

Final Answer:

The mass of the object is approximately:

$\boxed{7.2 \, \text{kg}}$

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Would you like additional details or explanations? Here are related questions:

1. What is the relationship between frequency and period in harmonic motion?
2. How does the spring constant affect the period of oscillation?
3. How would increasing the spring constant change the mass calculated in this problem?
4. What assumptions are made when analyzing simple harmonic motion?
5. How can damping forces affect the oscillation period?

Tip: Always double-check unit consistency when applying physical formulas to avoid calculation errors!