Calculating Frequency of Vibration for 0.3kg Mass Suspended from 200Nm Spring

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In summary, the frequency of vibration for a 0.3kg mass suspended from a 200Nm spring can be calculated using the formula f = (1/2π)√(k/m), where f is the frequency, k is the spring constant, and m is the mass. The spring constant can be determined by dividing the force applied to the spring by the displacement caused by that force, represented by the equation k = F/x. The frequency of vibration is affected by the mass suspended from the spring, as shown in the formula f = (1/2π)√(k/m). The spring constant directly affects the frequency of vibration, as seen in the formula f = (1/2π)√
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brenfox
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Homework Statement


A mass of 0.3kg is suspended from a spring 200Nm. If the mass is displaced by 10mm from its equilibrium position and released, for the resulting vibration, calculate:

a. the frequency of vibration.


Homework Equations


ω = √ k/m
f = ω/2∏

The Attempt at a Solution


ω=√ 200/0.3 = 25.82 rads-1

so f = ω / 2∏

f = 25.82/2∏ = 4.11Hz

Does this seem to be correct? Any help would be appreciated.
 
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1. What is the formula for calculating the frequency of vibration for a 0.3kg mass suspended from a 200Nm spring?

The formula for calculating the frequency of vibration for a 0.3kg mass suspended from a 200Nm spring is f = (1/2π)√(k/m), where f is the frequency, k is the spring constant (200Nm), and m is the mass (0.3kg).

2. How do you determine the spring constant for a given spring?

The spring constant can be determined by dividing the force applied to the spring by the displacement caused by that force. This can be represented by the equation k = F/x, where k is the spring constant, F is the force, and x is the displacement.

3. Is the frequency of vibration affected by the mass suspended from the spring?

Yes, the frequency of vibration is affected by the mass suspended from the spring. The formula for frequency of vibration (f = (1/2π)√(k/m)) shows that as mass increases, frequency decreases, and vice versa.

4. How does the spring constant affect the frequency of vibration?

The spring constant directly affects the frequency of vibration. As the spring constant increases, the frequency also increases, and vice versa. This can be seen in the formula f = (1/2π)√(k/m), where k is the spring constant.

5. Can other factors, such as temperature, affect the frequency of vibration for a given mass and spring?

Yes, other factors such as temperature can affect the frequency of vibration for a given mass and spring. Changes in temperature can cause the spring constant to change, which in turn affects the frequency of vibration. Additionally, changes in temperature can also affect the mass of an object, which would also impact the frequency of vibration.

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