Answer:
(E) It would increase by a factor of 2.
Explanation:
Maximum speed (v) is given by:
[tex]v = \omega *A[/tex]
Where ω is the angular frequency and A is the amplitude.
The angular frequency of a spring-mass system is given by:
[tex]\omega = \sqrt{\frac{k}{m}}[/tex]
Where k is the spring constant and m is the mass of the block attached to the spring.
Therefore, maximum speed can be written as:
[tex]v= A\sqrt{\frac{k}{m}}\\[/tex]
Since mass and amplitude are constant values, a relationship between maximum velocity and spring constant can be defined as:
[tex]v =C \sqrt{k}[/tex]
There is a linear relationship between maximum velocity and the square root of the spring constant. Therefore if the spring constant is increased by a factor of 4, the velocity is increased by a factor of the square root of 4, which is 2.
The answer is (E) It would increase by a factor of 2.
