Spring Force (Hooke's Law) Video Lessons

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Problem: T = 2πMkThe period of an object oscillating on the end of a spring is given by the formula:Here, the spring constant k comes from the usual definition by Hooke’s law, in terms of the force of the spring at some displacement from the equilibrium position x1:F = -k (x-x0)If we let M denote the mass of the object oscillating, this accurately describes an ideal situation in which springs are massless. There is actually a correction when we consider the case of springs whose mass of the springs, then the effective mass M (which we plug into the above formula) is defined by:M = MG + Ms/3We will also make use of the potential energy stored in a spring:U = ½ k (x-x0)2Note that the kinetic energy also uses the same effective mass M in place of the mass of the glider.Effective Spring Constant: In Part 1, you measured the keffective fo the two springs acting together. If the two springs k1 and k2 individually, how would they combine to get keff?

FREE Expert Solution

Hooke's law:

Fspring=-kx

Both the springs will experience a force, F.

For spring 1, we'll have:

F=k1x1

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Problem Details

T = 2πMk

The period of an object oscillating on the end of a spring is given by the formula:

Here, the spring constant k comes from the usual definition by Hooke’s law, in terms of the force of the spring at some displacement from the equilibrium position x1:
F = -k (x-x0)


If we let M denote the mass of the object oscillating, this accurately describes an ideal situation in which springs are massless. There is actually a correction when we consider the case of springs whose mass of the springs, then the effective mass M (which we plug into the above formula) is defined by:
M = MG + Ms/3

We will also make use of the potential energy stored in a spring:
U = ½ k (x-x0)2

Note that the kinetic energy also uses the same effective mass M in place of the mass of the glider.

Effective Spring Constant: In Part 1, you measured the keffective fo the two springs acting together. If the two springs k1 and k2 individually, how would they combine to get keff?

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