# Spring and energy problem

1. Apr 13, 2006

### nophun6

My question involves a spring configuration

For this configuration, the maximum displacement is .20m
Here is a graph of position vs time:

a) If m= 1.0 kg, calculate the value of the spring constant
b) Calculate the maximum value of both KE and PE
c) caluclate the total E

for a) F= -kx and F= ma so ma=-kx but how do i find acceleration?
for b) I know PE = 1/2 kx^2 and KE = 1/2mv^2 but I dont know what v is?
c) E = KE + PE correct?

2. Apr 13, 2006

### Staff: Mentor

Hint: How are the period of the motion, the mass, and the spring constant related?
Hint: Energy is conserved.
Sure.

3. Apr 13, 2006

### matt.o

The graph of position vs time looks suspiciously like a cosine function to me. Can you figure out how to relate position and time using this observation? If you can, you should be able to work out the velocity and acceleration.

4. Apr 14, 2006

### nophun6

Hmm, well the period is: T = 2(3.14) square root of (mass / spring constant)
and F= -kx
We are given the mass and the maximum displacemnt, A.
I still need help connecting the dots, I just cant see how to find the spring constant, k.

5. Apr 14, 2006

### Hootenanny

Staff Emeritus
(a) You need to use your equation

$$T = 2\pi\sqrt{\frac{m}{k}$$

You can read the time-period off the graph (time taken for one complete cycle) and you are given m, therefore the only unknown is k. Simply re-arrange the above equation to make k the subject and solve for k.

Regards,
-Hoot