Simple Harmonic Motion: Equivalent force constant of springs

Two springs with the same unstretched length, but different force constants and are attached to a block with mass on a level, frictionless surface. Calculate the effective force constant in each of the three cases depicted in the figure.

a). Express your answer in terms of the variables k1, m, k2
k_eff -c =

b) An object with mass , suspended from a uniform spring with a force constant , vibrates with a frequency . When the spring is cut in half and the same object is suspended from one of the halves, the frequency is . What is the ratio ?
Express your answer in terms of the variables k and m

**Any solution I have attempted to part B has prompted an automatic response of "answer does not depend on the variable k or m" Which confuses me to no end.

Any help on this problem would be VERY appreciated.

See attached file.
In Fig. 15-36, two springs are joined and connected to a block of mass 0.245 kg that is set oscillating over a frictionless floor. The springs each have spring constant k=6430 N/m . What is the frequency of the oscillations?

Prove that when two springs are attached one at the end of the other, the coefficient of the final spring becomes
1 / (1/k1 + 1/k2 ) where k1 and k2 are the coefficient of the two individual springs.
Then consider two systems of springs, one in which a mass m is attached two the end of two springs which a

Show that the values of w^2 (omega^2) for the three simpleharmonic oscillations (a), (b), (c) in the diagram (Attached) are in the ratio 1:2:4.
I said for a) that w^2 = s/2m (since the spring stiffness intuitively I think must be 1/2 less than just a single spring)
b) w^2 = s/m
c) w^2 = 2s/m
Which gives a ratio of 0

An 0.50 kg object is attached to one end of a spring, and the system is set into simpleharmonic motion. The displacement x of the object as a function of time is shown in the drawing below. With the aid of this data, determine the following values.
(a) amplitude A of the motion
(b) angular frequency
(c) spring c

Please see attachment. Thanks.
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Many real springs are more easily stretched than compressed. We can represent this by using different spring constants for and for . As an example, consider a spring that exerts the following restoring force:
A mass on a frictionless, horizontal surface is attached to this spring,

See attached file for full problem description.
1. Consider the four equivalent ways to represent simple harmonic motion in one dimension:
To make sure you understand all of these, show that they are equivalent by proving the following implications: I-->II--> III--> IV. For each form, given an expression for the constants (C

2. A spring with a 4-kg mass has natural length 1 m and is maintained stretched to a length of 1.3 m by a force of 24.3 N. If the spring is compressed to a length of 0.8 m and then released with zero velocity, find the position of the mass at any time t.
10. As in Exercise 9, consider a spring with mass m, spring constant k,

If i had two spring coupled to one mass with each end of the springs fixed.
|---spring---{mass}--spring----|
neglecting friction and gravity, if the mass is displaced horizontally. would it oscillate forever? if not how can u get the maximum amplitude of oscillation for a given period of time before it