Answer:
The magnitude of the restoring force per unit mass is 5.175 m/s².
Explanation:
To solve the question, we note that from Hooke's law
F = -k·x
Where:
F = Restoring force
k = Constant of restoration and
x = Displacement of the particle
Therefore when we have, F = m × a, this gives
m × a = -k·x or
a  = [tex]-\frac{k}{m} \times x[/tex]
That is the restoring force per unit mass is given by;
a  = [tex]-\frac{k}{m} \times x[/tex]
Where:
a = Acceleration
m = mass of the object.
For a given mass, [tex]\frac{k}{m}[/tex] is also constant
Therefore, when a  = 7.9 m/s²
x = 3.2 cm = , we have
a  = [tex]-\frac{k}{m} \times x[/tex] → 7.9 m/s² =  [tex]-\frac{k}{m}[/tex] × ‪0.032‬ m or
[tex]\frac{k}{m}[/tex] = (7.9 m/s²)/(0.032‬ m ) = 225
Therefore when x = 2.30 cm = 0.023, we have
a  = [tex]-\frac{k}{m} \times x[/tex]  = 225×0.023 m =  5.175 m/s²
The  restoring  force per unit mass = 5.175 m/s².
