What is the period of oscillation when the loaded car hits the bump?
Understand the Problem
The question is asking for the period of oscillation of a car when it encounters a bump, considering the car's mass and the additional mass of the adults. This involves understanding how mass affects oscillatory motion and possibly applying concepts from physics regarding simple harmonic motion.
Answer
$$ T = 2\pi \sqrt{\frac{m_c + m_a}{k}} $$
Answer for screen readers
The period of oscillation is given by the formula: $$ T = 2\pi \sqrt{\frac{m_c + m_a}{k}} $$
Steps to Solve
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Identify the total mass First, we need to find the total mass of the car including the adults. Let’s say the mass of the car is $m_c$ and the mass of the adults is $m_a$. The total mass $m_{total}$ will be: $$ m_{total} = m_c + m_a $$
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Determine the spring constant Next, we need to establish the spring constant $k$ of the car's suspension system. The spring constant can be found through experimentation or given in the problem.
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Use the formula for the period of oscillation The period of oscillation $T$ for a mass-spring system is given by the formula: $$ T = 2\pi \sqrt{\frac{m_{total}}{k}} $$ Here, $m_{total}$ is the total mass calculated in step 1, and $k$ is the spring constant from step 2.
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Calculate the period Substitute the values of $m_{total}$ and $k$ into the formula to find the period $T$.
The period of oscillation is given by the formula: $$ T = 2\pi \sqrt{\frac{m_c + m_a}{k}} $$
More Information
The period of oscillation indicates how long it takes the car to complete one full cycle of motion when encountering a bump. This concept is essential in understanding how vehicles respond to uneven surfaces and is a practical application of simple harmonic motion mechanics.
Tips
- Forgetting to include both the mass of the car and the mass of the adults when calculating the total mass.
- Misinterpreting the spring constant which could lead to incorrect calculations of the period.
- Confusing the units of mass and spring constant, which could lead to errors in the final output.
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