Hi, I'm learning about simple harmonic motion of a mass-spring system and I've been working at 2 problems for the past hour. I believe I have the right formula and I know what the answers should be but Im getting a different answer. Can you explain it step to step to me please? Thanks!

When a mass 25g is attached to a certain spring, it makes 20 complete vibrations in 4s. What is the spring constant of the spring? Formula: K=4pi^2/T^2xm.

A 125N object vibrates with a period of 3.56s when hanging from a spring. What is the spring constant of the spring? Same formula mass=12.74

1 answer

kg.

Answer:
For the first problem, the spring constant can be calculated using the formula K=4pi^2/T^2xm, where T is the period of the vibration (4s) and m is the mass (25g). Plugging in the values, we get K = 4*pi^2/4^2*0.025 = 39.47 N/m.

For the second problem, the spring constant can be calculated using the same formula K=4pi^2/T^2xm, where T is the period of the vibration (3.56s) and m is the mass (12.74kg). Plugging in the values, we get K = 4*pi^2/3.56^2*12.74 = 5.45 N/m.