Completing a lab assignment and was wondering if anyone could look over my work.

A 5.0-g mass is sandwiched between two springs with spring constants k1 and k2. The mass is displaced 10 cm from its equilibrium position and makes sixteen complete oscillations in 1 s with no loss of mechanical energy. Calculate the period of the motion T, the angular frequency w, the sum of the spring constants k1+k2, and the mechanical energy E of the oscillator.

Using the information, I found that the period was equal to 1/16 because the frequency is equal to 1/T.
W=2pi/T
W=100.53 rads/s

W=(k/m)^(1/2)
k=m*w^2
k=50.53 kg/s^2

E=1/2 * k* A^2
E=1/2 * (50.53)*(.10)^2
E=12.76 J

Not really sure how to do the second part of the problem

2. The experiment is repeated, this time displacing the mass only one centimeter from the equilibrium position. Calculate the angular frequency w of the motion and the mechanical energy E of the oscillator.

new A = A/10

k and m unchanged
so omega unchanged
T unchanged
E = (1/2) *same k * (new A)^2
= old energy / 100

To solve the second part of the problem, where the mass is displaced one centimeter from the equilibrium position, you can follow a similar approach as before.

First, let's start with finding the angular frequency w of the motion:

w = 2π / T

Since we already know that the period T is 1/16 s (as we determined earlier), we can substitute that value into the equation and calculate the angular frequency:

w = 2π / (1/16)
w = 32π rad/s

So, the angular frequency w of the motion is 32π rad/s.

Now, let's calculate the mechanical energy E of the oscillator:

E = 1/2 * k * A^2

In this equation, k represents the sum of the spring constants k1 and k2, and A represents the displacement from the equilibrium position. We are given that the mass is displaced only one centimeter, which is 0.01 m.

To find the sum of the spring constants k1 and k2, we need additional information about the springs. If you have that information, you can substitute the appropriate values. Otherwise, if you do not have this information, it is not possible to calculate the sum of spring constants (k1 + k2) or the mechanical energy E of the oscillator.