Period of Motion: Find Mass 0.85kg Piston's Period of Motion

In summary, the period of motion can be calculated using the formula T = 2π√(m/k), where T is the period in seconds, m is the mass in kilograms, and k is the spring constant in Newtons per meter. To find the mass of an object in a period of motion, the formula m = (T/2π)^2 * k can be used. The mass must be in kilograms and the period must be in seconds for the formula to work correctly. Changing the mass will affect the period of motion, with an increase in mass resulting in a longer period and a decrease in mass resulting in a shorter period due to the inverse relationship. The spring constant also affects the period of motion, with a
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Coatesy
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The movement of a particular piston of mass 0.85kg may be modeled with a simple harmonic. Given that its acceleration is 8m/s when 10cm from the mid position. Find the period of the motion??

I found velocity to = 1.26m/s, but I am not even sure if i need to calculate the velocity.
 
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a=-(2πf)2x

We have a (= 8 m/s)
We know 2π (constant)
And we know x (= 10cm)

Rearrange to find f.

Period = 1/f
 
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1. What is the formula for calculating the period of motion?

The formula for calculating the period of motion is T = 2π√(m/k), where T is the period in seconds, m is the mass in kilograms, and k is the spring constant in Newtons per meter.

2. How do you find the mass of an object in a period of motion?

To find the mass of an object in a period of motion, you can use the formula m = (T/2π)^2 * k, where T is the period in seconds and k is the spring constant in Newtons per meter.

3. Can you use any unit for mass and period in the formula?

No, the mass must be in kilograms and the period must be in seconds for the formula to work correctly.

4. How does changing the mass affect the period of motion?

Increasing the mass will result in a longer period of motion, while decreasing the mass will result in a shorter period of motion. This is because the period is inversely proportional to the square root of the mass.

5. How does the spring constant affect the period of motion?

The spring constant affects the period of motion by directly impacting the stiffness of the spring. A higher spring constant will result in a shorter period of motion, while a lower spring constant will result in a longer period of motion.

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