Ablock of mass m attached to a horizontally mounted spring with spring constant k undergoes simple harmonic motion on a frictionless surface. how would the maximum speed of the block be affected if the spring constant was increased by a factor of 4 while holding the amplitude of oscillation constant?

The maximum speed would double

Explanation:

The maximum speed of a mass-spring system is given by:

where

is the angular frequency

A is the amplitude of the motion

The angular frequency in a spring-mass system is

where

k is the spring constant

m is the mass

Substituting inside the first equation,

In this problem:

- the spring constant is increased by a factor 4: k' = 4 k

- the amplitude remains constant: A' = A

So the new maximum speed would be

So, the maximum speed would double.