Oscillations Lab HELP ME PLEASE

[NotMySubject!]

Homework Statement

Please calculate the units for the spring constant k in two fashions. First, from
Hooke’s Law (eqn. 5 in lab manual), and then from the period equation for a spring
(eqn. 3). Please show that these units are compatible (i.e. mean the same thing).

Homework Equations

equation 5 k=Mg/x
equation 3 T=2$$\pi$$$$\sqrt{}M/k$$

The Attempt at a Solution

well i am pretty sure that Hooke's law give N/m but i have no idea how to show that the units for the second equation are compatible with the first...any ideas on how to figure this out?

 

[ideasrule]

Just plug in the units for M and T and isolate the units of k.

 

[kerimek]

Yes, both equations should give the same units for the spring constant k. Let's start by looking at the units for equation 5, k=Mg/x. The unit for mass (M) is in kilograms (kg), the unit for acceleration due to gravity (g) is in meters per second squared (m/s^2), and the unit for displacement (x) is in meters (m). Therefore, the units for k would be kg*m/s^2/m, which simplifies to kg/s^2. This is the same unit as N/m, which is the unit for the spring constant in Hooke's law.

Now, let's look at the units for equation 3, T=2\pi\sqrt{}M/k. The unit for time (T) is in seconds (s), the unit for mass (M) is in kilograms (kg), and the unit for the spring constant (k) is in N/m. Therefore, the units for k would be kg/s^2, which is the same unit as before. This shows that the units for k are compatible between the two equations.

To further understand this, let's substitute the units for k in equation 3, T=2\pi\sqrt{}M/(kg/s^2). This simplifies to T=2\pi\sqrt{}M*s^2/kg, which is the same as T=2\pi\sqrt{}M*N*s^2/m, which is the same as T=2\pi\sqrt{}M*N/m, which is the same as T=2\pi\sqrt{}(kg*m/s^2)*N/m, which is the same as T=2\pi\sqrt{}N, which is the same as T=2\pi. This shows that the units for the spring constant k in equation 3 are compatible with the units for k in equation 5, and they both mean the same thing.