1. Suppose the spring in Sample Problem A is replaced with a spring that stretches 36 cm from its equilibrium position.

a. What is the spring constant in this case?

b. Is this spring stiffer or less stiff than the one in Sample Problem A?

a. spring constant = 125 N/m

b. This spring is less stiff than the one in Sample Problem A.

Explanation:

P.S - The Sample Problem A is as follows :

Given - Sample Problem A - A load of 45 N attached to a spring that is

            hanging vertically stretches the spring 0.14 m. What is the spring

             constant?

            Suppose the spring in Sample Problem A is replaced with a spring  

            that stretches 36 cm from its equilibrium position.

To find - a. What is the spring constant in this case?

            b. Is this spring stiffer or less stiff than the one in Sample Problem A.

Proof -

As given,

Load = 45 N

Amplitude = 0.14 m

Let the spring constant = k

As we know that,

Load = k (Amplitude)

⇒45 = k(0.14)

⇒k = = 321.43

∴ we get

Spring constant in Sample problem A = 321.43

Now,

a.)

Given, Amplitude = 36 cm = 0.36 m

Let the spring constant = k₁

⇒45 = k₁ (0.36)

⇒k₁ = = 125 N/m

b.)

AS we can see that k₁  < k

⇒ This spring is less stiff than the one in Sample Problem A.

wavelength divides in half and speed stays the same.

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