5. The two springs from the problem above are reconnected to mass m as shown. Now what is the frequency of oscillation? 2 ellue m Fee ull
5. The two springs from the problem above are reconnected to mass m as shown. Now what is the frequency of oscillation? 2 ellue m Fee ull
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Can someone please explain it to me ASAP?!!! This is periodic motion
![**Problem: Determining the Frequency of Oscillation**
**Question:**
The two springs from the problem above are reconnected to mass \( m \) as shown. Now, what is the frequency of oscillation?
**Diagram:**
The diagram shows a mass \( m \) connected between two springs with spring constants \( k_1 \) and \( k_2 \). The spring \( k_1 \) is attached to the left of the mass, and the spring \( k_2 \) is attached to the right of the mass. Both springs are fixed at the opposite ends, forming a horizontal system.
To determine the frequency of oscillation (\( \omega \)) of the mass \( m \), we can start by noting that the springs are in series. The effective spring constant \( k \) of two springs in series is given by:
\[
\frac{1}{k} = \frac{1}{k_1} + \frac{1}{k_2}
\]
Simplifying this, we get:
\[
k = \frac{k_1 k_2}{k_1 + k_2}
\]
The frequency of oscillation is given by the formula:
\[
\omega = \sqrt{\frac{k}{m}}
\]
Substituting the effective spring constant \( k \) into the equation, we obtain the frequency of oscillation:
\[
\omega = \sqrt{\frac{\frac{k_1 k_2}{k_1 + k_2}}{m}} = \sqrt{\frac{k_1 k_2}{m(k_1 + k_2)}}
\]
Thus, the frequency of oscillation for the mass \( m \) connected to two springs with spring constants \( k_1 \) and \( k_2 \) is:
\[
\boxed{\omega = \sqrt{\frac{k_1 k_2}{m(k_1 + k_2)}}}
\]
This formula allows us to find the natural frequency of the system based on the given spring constants and mass.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11ad9986-04b0-4336-8340-a3038312afe8%2Ff730789b-c712-480e-bc78-44a2f7534e8d%2F9bs6yh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem: Determining the Frequency of Oscillation**
**Question:**
The two springs from the problem above are reconnected to mass \( m \) as shown. Now, what is the frequency of oscillation?
**Diagram:**
The diagram shows a mass \( m \) connected between two springs with spring constants \( k_1 \) and \( k_2 \). The spring \( k_1 \) is attached to the left of the mass, and the spring \( k_2 \) is attached to the right of the mass. Both springs are fixed at the opposite ends, forming a horizontal system.
To determine the frequency of oscillation (\( \omega \)) of the mass \( m \), we can start by noting that the springs are in series. The effective spring constant \( k \) of two springs in series is given by:
\[
\frac{1}{k} = \frac{1}{k_1} + \frac{1}{k_2}
\]
Simplifying this, we get:
\[
k = \frac{k_1 k_2}{k_1 + k_2}
\]
The frequency of oscillation is given by the formula:
\[
\omega = \sqrt{\frac{k}{m}}
\]
Substituting the effective spring constant \( k \) into the equation, we obtain the frequency of oscillation:
\[
\omega = \sqrt{\frac{\frac{k_1 k_2}{k_1 + k_2}}{m}} = \sqrt{\frac{k_1 k_2}{m(k_1 + k_2)}}
\]
Thus, the frequency of oscillation for the mass \( m \) connected to two springs with spring constants \( k_1 \) and \( k_2 \) is:
\[
\boxed{\omega = \sqrt{\frac{k_1 k_2}{m(k_1 + k_2)}}}
\]
This formula allows us to find the natural frequency of the system based on the given spring constants and mass.
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