Question

Select the correct expression that gives the block's acceleration at a displacement x from the equilibrium position. Note that x can be either positive or negative; that is, the block can be either to the right or left of its equilibrium position.
a. a=−kx
b. a=kx
c. a=kmx
d. a=−kmx

Answer 1

Answer:

d. a=−k/mx

Explanation:

To know what is the correct expression for the acceleration you take into account the second Newton law, that is:

$F=ma$ ( 1 )

next, you equal the expression ( 1 ) to the force in a mass-string system, that is F=-kx.

$ma=-kx\\\\a=-\frac{kx}{m}$

hence, the acceleration is:

d. a=−kmx

Answer 2

Answer:

a = -kmx ( D )

Explanation:

Acceleration = velocity / time

velocity = displacement / time

but since the block is at equilibrium and X which is displacement can be either negative or positive

applying newton law of motion

F = ma

considering the force acting on the object

ma = - kx

hence a = -kx/m