Ap Physics 1 algebra based Oscillation

Question

You set up a simple harmonic motion by attaching a mass of 100 g to a spring. To find the spring constant, you hang the mass to the spring vertically and find the spring stretches 10 cm. Find k of the spring.

Answer 1

Classic problem in undergraduate vibrations. Are you going to be an engineer? LOL

Anyway, as long as the system is moving, the motion is given by

 

F = ma + kx

 

If the system has no force acting on it, and it's not moving, you have

 

0 = mg + kx

 

where m = 0.1 kg (we have to be unit-correct)

g = -9.8 m/s^2 (most teachers call it 10 any more, and the negative sign is for going down)

and x = 0.01 m

 

So.

 

1 kg-m/s^2 = (0.01 m) k

 

that makes k = 100 kg/s^2

 

The units look funky. But trust me, that's units of force/distance. LOL