Question

A block of mass m attached to a horizontally mounted spring with spring constant ???? 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?

(A) It would increase by a factor of 4.
(B) It would decrease by a factor of 12.
(C) It would decrease by a factor of 14.
(D) It would remain unchanged.
(E) It would increase by a factor of 2.

Answer 1

(E) It would increase by a factor of 2.

Step-by-step explanation:

Maximum speed (v) is given by:

`v = \omega *A`

Where ω is the angular frequency and A is the amplitude.

The angular frequency of a spring-mass system is given by:

`\omega = \sqrt{(k)/(m)}`

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:

`v= A\sqrt{(k)/(m)}\\`

Since mass and amplitude are constant values, a relationship between maximum velocity and spring constant can be defined as:

`v =C √(k)`

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.