Frequency of Vibration for a Block Supported by Two Springs

[Big-J]

Homework Statement

A block of mass m is supported by two identical parallel springs, each with spring stiffness constant k. What will be the frequency of vibration?

Homework Equations

f = 1/[2*pi*sqrt(m/k)]

The Attempt at a Solution

I am just curious how the fact that there are two springs supporting m instead of one will affect my answer (which should be in terms of m and k.)

Thanks!

 

[G01]

1. The two springs will act like a different spring with it's own k constant. Thus, if you find the frequency of this bigger, imaginary spring, you'll find the frequency of the two springs. Do you have an idea how the k constant of this imaginary spring will compare to the k constant of the two real springs?

2. You can also think of this problem by assuming each spring supports half the mass of the block and then proceeding to find the frequency of one of those springs, since they will both have the same frequency.

Either method will give the same answer. So, can you follow either 1. or 2. above? Does this help shed light on how the frequency will change?

 

[Big-J]

Yeah your #2 made a lot of sense to me.

Thanks for your help. I appreciate it.