Oscillating Springs: Finding Frequency w/ k1, k2, & m

In summary, the problem is determining the frequency of vibrations for a mass connected to two springs with stiffness k1 and k2. The relevant equation is f=(1/2pi)sqrt(k/m). The attempt at a solution involves finding the combined force equation for the two springs and equating it to the force at the ends.
  • #1
patrick4
1
0

Homework Statement



I've had some problems trying to work through this problem:

Two springs of stiffness k1 and k2 are attached in succession to a mass m. What is the frequency of vibrations in terms of the spring stiffness k1 and k2 and the mass m?

Homework Equations



f=(1/2pi)sqrt(k/m)

I think that is the only relevant equation, but I am not entirely sure.

The Attempt at a Solution



I am confused at weather or not I need to multiply or add the two spring constants. Or, if I need to make two separate equations with the frequencies being constant in both equations.

I tried to relate it to the energy of a spring, but I didn't have a displacement so that equation would not work.

Any help would be greatly appreciated, Thanks!:smile:
 
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  • #2
try 2 dispalcement variables
the end of the first spring
the end of the 2nd spring

write down the force vs distance equation of each spring & so find the expression for the 2 combined by equating the force
 

FAQ: Oscillating Springs: Finding Frequency w/ k1, k2, & m

1. What is an oscillating spring?

An oscillating spring is a mechanical system consisting of a mass attached to a spring that is able to move back and forth in a repetitive motion when disturbed from its equilibrium position.

2. How do you find the frequency of an oscillating spring?

The frequency of an oscillating spring can be found by using the formula f = 1/(2π) * √(k/m), where k is the spring constant and m is the mass attached to the spring.

3. What is the significance of k1, k2, and m in finding the frequency of an oscillating spring?

K1 and k2 represent the two different spring constants in a compound spring system, while m represents the mass attached to the spring. These values are used in the frequency formula to calculate the frequency of the oscillating spring.

4. What factors can affect the frequency of an oscillating spring?

The frequency of an oscillating spring can be affected by the mass attached to the spring, the spring constant, and the amplitude of the oscillations. Other factors such as air resistance and friction can also play a role in altering the frequency.

5. How does the frequency of an oscillating spring relate to its period?

The frequency and period of an oscillating spring are inversely proportional. This means that as the frequency increases, the period decreases, and vice versa. The period is the time it takes for one complete cycle of the oscillation, while the frequency is the number of cycles per second.

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