How Do You Calculate the Frequency and Maximum Velocity of a Mass on a Spring?

[Kev1n]

1. A mass attached to the lower end of a vertical spring causes the spring to extend 25mm to its equilibrium position. The mass is then displaced a further 20mm and released. A trace of the vibration and time measurements are taken. From these measurements it can be seen that the displacement from equilibrium position is 19.2 when the time is 0.05s
A. Calculate the expected frequeny of vibration, B. Calculate the maximm velocity of the mass. I have struggled here as ther is no (k) for the spring or mass
It would be appreciated if anyone could havea look over at my attempt and comment, thanks



2. w=sqrt(k/m), mg=kl, m=kl/g



3. A. w=sqrt (k/m), l = 25mm so 0.25m, g =9.81
m = l/g = 0.025
Basically now can see where to go without k

 

[SeanGillespie]

To find the period of a spring you do not need to know the mass or the spring constant.

Substitute the calculation for the spring constant into the equation for the period, you should find that you are left with only variables you are able to calculate.

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

k = $$\frac{F}{x}$$

And think about the calculation for F.

 

[kerimek]

so substitute in the formula for k = w^2m, w = 2*pi*f, so f = sqrt(k/m)/(2*pi)


B. To calculate the maximum velocity of the mass, we can use the formula vmax = A*w, where A is the amplitude of the vibration and w is the angular frequency. In this case, A = 19.2mm = 0.0192m, and we can use the same value for w that we calculated in part A. So, vmax = 0.0192 * sqrt(k/m)/(2*pi) = 0.0096*sqrt(k/m) m/s.

As you mentioned, there is no given value for k or mass in this scenario, so we cannot give a specific numerical answer for the frequency or maximum velocity. However, we can use the given information and formulas to determine the relationship between k and m, and ultimately the frequency and maximum velocity.