SHM Question: What is the maximum extension of the spring?

[Alex Cooper]

Homework Statement

A 50g block is attached to a vertical spring whose stiffness constant is 9N/m. The block is released at the position where the spring is unextended. What is the maximum extension of the spring? How long does it take the block to reach the lowest point?

Homework Equations

Fsp=-kx
T=2pi(sqrtm/k)
KE=1/2mv^2
Usp = mgh

The Attempt at a Solution

I found the time it took to reach the lowest point but cannot seem to find the first portion of the question
Here is what I did for the time it took to reach the lowest point
T=2pi(sqrtm/k)
=2pi(sqrt0.05/9)
=0.468s/2
=0.23s

 

[gneill]

Hello Alex, Welcome to Physics Forums.

I found the time it took to reach the lowest point but cannot seem to find the first portion of the question
Here is what I did for the time it took to reach the lowest point
T=2pi(sqrtm/k)
=2pi(sqrt0.05/9)
=0.468s/2
=0.23s

You should be a bit more careful with your notation. When you introduced dividing by two in the second to last line, the quantity is no longer equal to the quantity above. You should also indicate the logic behind what you're doing with a comment.

That said, the division by two is not correct here. It's not a half cycle from the equilibrium point to an extreme. A half cycle would be a trip from equilibrium to extreme and then back to the equilibrium point (the block would then continue through the equilibrium point and continue upwards to a higher extreme point, then return to the equilibrium point to complete a full cycle). So choose another value other than "2".

For the distance to the lower extreme, consider a conservation of energy approach. Your Relevant equations did not include the potential energy for a spring, but you should have that in your text or notes.