# Oscillations: The spring with varying force constant

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, displaced to by stretching the spring and released.

1) Find the period of the motion.

Express your answer in terms of and .

2) Does the period depend on ?

yes

no

3) Are the oscillations simple harmonic?

yes

no

4) What is the most negative value of that the mass reaches?

5) Is the oscillation symmetric about the point ?

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https://brainmass.com/physics/energy/oscillations-spring-varying-force-constant-74058

#### Solution Preview

Please see the attachment

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, displaced to by stretching the spring and released.

I think the force is - kx for x > 0

And - 2kx for x < ...

#### Solution Summary

The spring is having different force constants for stretching and compressing, The period is calculated and other four parts are discussed and answered.