The max speed of a 3.1 kg mass attached to a spring is .68 m/s and the max force exerted on the mass is 11N. What is the amplitude of motion on the mass? What is the force constant of the spring? And what is the frequency of oscillation?

I can do the work, just need the formulas!

Does anyone know how to do this question

The following seem to work for part a)

F=ma

And

Vmax^2 / amax

for part b) once you have the amplitude everything else is easy to find

To find the amplitude of motion, force constant of the spring, and frequency of oscillation, we can use the given information about the mass, maximum speed, and maximum force.

1. Amplitude of motion (A):
The amplitude is the maximum displacement from the equilibrium position. In simple harmonic motion, the amplitude is equal to the maximum distance the mass moves away from the equilibrium position.

To find the amplitude, we can use the equation:
A = vmax / ω

Where A is the amplitude, vmax is the maximum speed, and ω is the angular frequency.

Given that vmax = 0.68 m/s, we still need to find the angular frequency.

2. Angular frequency (ω):
The angular frequency is related to the frequency (f) by the equation:

ω = 2πf

To find the frequency, we divide the maximum speed by the amplitude:
vmax = Aω

Rearranging the equation for ω, we get:
ω = vmax / A

Now we can substitute the values:
ω = 0.68 m/s / A

But we still need to find the amplitude (A).

3. Force constant of the spring (k):
The force exerted by a spring is given by Hooke's law:

F = -kx

Where F is the force, k is the force constant, and x is the displacement from the equilibrium position. In simple harmonic motion, the maximum force exerted on the mass is equal to k times the amplitude.

The given maximum force is 11 N, so we have:
11 N = kA

Now we need to find the force constant (k) and the amplitude (A).

4. Frequency of oscillation (f):
The frequency of oscillation is the number of complete cycles (oscillations) per unit of time. It is related to the angular frequency by the equation:

f = ω / (2π)

So we need to find ω to calculate the frequency.

Now let's solve these equations step by step:

Step 1: Find the amplitude (A):
Using the equation A = vmax / ω, we need to find the angular frequency (ω) first.

Step 2: Find the angular frequency (ω):
Using the equation ω = vmax / A, substitute the given values of vmax and A to find ω.

Step 3: Find the force constant of the spring (k):
Using the equation 11 N = kA, substitute the given values of the maximum force and amplitude to find k.

Step 4: Find the frequency of oscillation (f):
Using the equation f = ω / (2π), substitute the obtained value of ω to find the frequency.

By following these steps, we can calculate the amplitude, force constant of the spring, and frequency of oscillation based on the given information.