How Does Doubling the Springs Affect the Oscillation Period?

[map7s]

There is a spring with one end attached to a wall and the other end attached to a mass of 1.19 kg. On the other side of the mass is another spring whose other end is attached to another wall. The springs are identical and have a spring constant value of 49.7 N/m. What is the period?

I drew out a picture and I know that I need to use the equation T=2pi*square root of mass/k but with some modifications to the k. At first I thought that, with the spring being identical on both sides, the spring force would cancel out, but obviously that was wrong. How would I be able to use a modified form of this equation to solve for the period?

 

[berkeman]

There might be a simplification that would help. In the linear region, the spring force is just F=kx, where x is the displacement, regardless of whether it is compression or tension. If you displace the block to the right some distance, that is seen by one spring as compression and by the other as tension, right? What is the total force on the block from the 2 springs, expressed in terms of the value k and the displacement?...

 

[map7s]

Would it just be F=2kx ?

 

[berkeman]

Would it just be F=2kx ?

Yep. So that simplifies working out the answer for the period, right?

 

[map7s]

So, would I have to use the equation T=2pi*square root of m/(2k) ?

 

[OlderDan]

So, would I have to use the equation T=2pi*square root of m/(2k) ?

That will do it.