Particle P in the metal sheet preforms simple harmonic oscillations. When the displacement of P is 3.2cm, the magnitude of its restoring force is 7.9 m/s^2. Calculate the magnitude of the net restoring force on P when it's displacement is 2.3cm

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  =

That is the restoring force per unit mass is given by;

a  =

Where:

a = Acceleration

m = mass of the object.

For a given mass, is also constant

Therefore, when a  = 7.9 m/s²

x = 3.2 cm = , we have

a  = → 7.9 m/s² =   × ‪0.032‬ m or

= (7.9 m/s²)/(0.032‬ m ) = 225

Therefore when x = 2.30 cm = 0.023, we have

a  =  = 225×0.023 m =  5.175 m/s²

The  restoring  force per unit mass = 5.175 m/s².

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