How Do You Calculate Oscillation Frequency for a Mass with Two Springs?

[TDAWG12489]

Homework Statement

A 8.3 kg mass slides on a frictionless surface
and is attached to two springs with spring
constants 28 N/m and 62 N/m that are on either side of the mass.


Find the frequency of oscillation. Answer
in units of Hz.

Homework Equations

(2pi sqrt(m/k))^-1

The Attempt at a Solution

subtract the constants from each other to find the coonstant of the system. use this in the equation above. I got about .322Hz is this right?

 

[OlderDan]

You need to rethink the combined effect of the two springs. At equilibrium, each spring is pulling the mass with the same amount of force. What happens to each of those forces when the mass is moved to one side?

 

[m2003]

I would first clarify that the given information is for a simple harmonic motion system with two springs and a mass on a frictionless surface. I would then proceed to explain that the frequency of oscillation for a simple harmonic motion can be calculated using the equation (2π√(m/k))^-1, where m is the mass and k is the spring constant of the system.

Next, I would show the steps to calculate the frequency for the given system. Since there are two springs with different spring constants, the effective spring constant of the system can be found by adding the reciprocals of the individual spring constants. In this case, the effective spring constant would be (1/28 + 1/62)^-1 = 19.2 N/m.

Substituting this value and the given mass of 8.3 kg into the frequency equation, we get (2π√(8.3/19.2))^-1 = 0.322 Hz. Therefore, the frequency of oscillation for the given system is 0.322 Hz.

I would also mention that the frequency of oscillation is a measure of how quickly the system repeats its motion and is dependent on the mass and stiffness of the system. A higher frequency would indicate a faster oscillation and a lower frequency would indicate a slower oscillation.